Forecasting the Time Series of Sunspot Numbers
Aguirre, L. A.; Letellier, C.; Maquet, J.
2008-05-01
Forecasting the solar cycle is of great importance for weather prediction and environmental monitoring, and also constitutes a difficult scientific benchmark in nonlinear dynamical modeling. This paper describes the identification of a model and its use in the forecasting the time series comprised of Wolf’s sunspot numbers. A key feature of this procedure is that the original time series is first transformed into a symmetrical space where the dynamics of the solar dynamo are unfolded in a better way, thus improving the model. The nonlinear model obtained is parsimonious and has both deterministic and stochastic parts. Monte Carlo simulation of the whole model produces very consistent results with the deterministic part of the model but allows for the determination of confidence bands. The obtained model was used to predict cycles 24 and 25, although the forecast of the latter is seen as a crude approximation, given the long prediction horizon required. As for the 24th cycle, two estimates were obtained with peaks of 65±16 and of 87±13 units of sunspot numbers. The simulated results suggest that the 24th cycle will be shorter and less active than the preceding one.
Comparison of New and Old Sunspot Number Time Series
Cliver, E. W.
2016-11-01
Four new sunspot number time series have been published in this Topical Issue: a backbone-based group number in Svalgaard and Schatten ( Solar Phys., 2016; referred to here as SS, 1610 - present), a group number series in Usoskin et al. ( Solar Phys., 2016; UEA, 1749 - present) that employs active day fractions from which it derives an observational threshold in group spot area as a measure of observer merit, a provisional group number series in Cliver and Ling ( Solar Phys., 2016; CL, 1841 - 1976) that removed flaws in the Hoyt and Schatten ( Solar Phys. 179, 189, 1998a; 181, 491, 1998b) normalization scheme for the original relative group sunspot number (RG, 1610 - 1995), and a corrected Wolf (international, RI) number in Clette and Lefèvre ( Solar Phys., 2016; SN, 1700 - present). Despite quite different construction methods, the four new series agree well after about 1900. Before 1900, however, the UEA time series is lower than SS, CL, and SN, particularly so before about 1885. Overall, the UEA series most closely resembles the original RG series. Comparison of the UEA and SS series with a new solar wind B time series (Owens et al. in J. Geophys. Res., 2016; 1845 - present) indicates that the UEA time series is too low before 1900. We point out incongruities in the Usoskin et al. ( Solar Phys., 2016) observer normalization scheme and present evidence that this method under-estimates group counts before 1900. In general, a correction factor time series, obtained by dividing an annual group count series by the corresponding yearly averages of raw group counts for all observers, can be used to assess the reliability of new sunspot number reconstructions.
Salient Features of the New Sunspot Number Time Series
Ahluwalia, H. S.; Ygbuhay, R. C.
2016-12-01
Recently Clette et al. (Space Sci. Rev. 186, 35, 2014) completed the first revision of the international sunspot number SSN(V2) since its creation by Wolf in 1849 SSN(V1) starting in 1700 and ending in May 2015. The yearly values of SSN(V2) are larger than those of SSN(V1) but the secular trend in their timelines both exhibit a gradual descent after Cycle 21 minimum resulting in greatly reduced activity for Cycle 24. It has two peaks; one in 2012 due to activity in the north hemisphere (NH) and the other in 2014 due to excess activity in the south hemisphere (SH). The N-S excess of hemispheric SSNs is examined for 1950 - 2014, in relation to the time variations of the solar polar field for 1976 - 2015, covering five complete solar cycles (19 - 23) and parts of the bordering two (18, 24). We find that SH tends to become progressively more active in the declining phase of the cycles reaching an extreme value that gave rise to a second higher peak in October 2014 in the smoothed SSNs accompanied by a strong solar polar field in SH. There may be a Gleissberg cyclicity in the asymmetric solar dynamo operation. The continuing descent of the secular trend in SSNs implies that we may be near a Dalton-level grand minimum. The low activity spell may last well past 2060, accompanied by a stable but reduced level of the space weather/climate. Fourier spectrum of the time domain of SSNs shows no evidence of the 208 year/cycle (ypc) (DeVries/Suess cycle) seen in the cosmogenic radionuclide ({}^{10}Be) concentration in the polar ice cores and {}^{14}C record in trees indicating that 208 ypc peak may be of non-solar origin. It may arise from the climate process(es) that change(s) the way radionuclides are deposited on polar ice. It should be noted that we only have {˜} 400 years of SSN data, so it is possible that DeVries/Suess cycle is really driven by the Sun but for now we do not have any evidence of that; there is no known physical process linking 208 ypc to solar dynamo
Chattopadhyay, Goutami; 10.1140/epjp/i2012-12043-9
2012-01-01
This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).
Looking for granulation and periodicity imprints in the sunspot time series
Lopes, Ilidio
2015-01-01
The sunspot activity is the end result of the cyclic destruction and regeneration of magnetic fields by the dynamo action. We propose a new method to analyze the daily sunspot areas data recorded since 1874. By computing the power spectral density of daily data series using the Mexican hat wavelet, we found a power spectrum with a well-defined shape, characterized by three features. The first term is the 22 yr solar magnetic cycle, estimated in our work to be of 18.43 yr. The second term is related to the daily volatility of sunspots. This term is most likely produced by the turbulent motions linked to the solar granulation. The last term corresponds to a periodic source associated with the solar magnetic activity, for which the maximum of power spectral density occurs at 22.67 days. This value is part of the 22-27 day periodicity region that shows an above-average intensity in the power spectra. The origin of this 22.67 day periodic process is not clearly identified, and there is a possibility that it can be...
LOOKING FOR GRANULATION AND PERIODICITY IMPRINTS IN THE SUNSPOT TIME SERIES
Energy Technology Data Exchange (ETDEWEB)
Lopes, Ilídio [Centro Multidisciplinar de Astrofísica, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Silva, Hugo G., E-mail: ilidio.lopes@tecnico.ulisboa.pt, E-mail: hgsilva@uevora.pt [Departamento de Física, ECT, Instituto de Ciências da Terra, Universidade de Évora, Rua Romão Ramalho 59, 7002-554 Évora (Portugal)
2015-05-10
The sunspot activity is the end result of the cyclic destruction and regeneration of magnetic fields by the dynamo action. We propose a new method to analyze the daily sunspot areas data recorded since 1874. By computing the power spectral density of daily data series using the Mexican hat wavelet, we found a power spectrum with a well-defined shape, characterized by three features. The first term is the 22 yr solar magnetic cycle, estimated in our work to be 18.43 yr. The second term is related to the daily volatility of sunspots. This term is most likely produced by the turbulent motions linked to the solar granulation. The last term corresponds to a periodic source associated with the solar magnetic activity, for which the maximum power spectral density occurs at 22.67 days. This value is part of the 22–27 day periodicity region that shows an above-average intensity in the power spectra. The origin of this 22.67 day periodic process is not clearly identified, and there is a possibility that it can be produced by convective flows inside the star. The study clearly shows a north–south asymmetry. The 18.43 yr periodical source is correlated between the two hemispheres, but the 22.67 day one is not correlated. It is shown that toward the large timescales an excess occurs in the northern hemisphere, especially near the previous two periodic sources. To further investigate the 22.67 day periodicity, we made a Lomb–Scargle spectral analysis. The study suggests that this periodicity is distinct from others found nearby.
Deming, Drake; Boyle, Robert J.; Jennings, Donald E.; Wiedemann, Gunter
1988-01-01
The use of the extremely Zeeman-sensitive IR emission line Mg I, at 12.32 microns, to study solar magnetic fields. Time series observations of the line in the quiet sun were obtained in order to determine the response time of the line to the five-minute oscillations. Based upon the velocity amplitude and average period measured in the line, it is concluded that it is formed in the temperature minimum region. The magnetic structure of sunspots is investigated by stepping a small field of view in linear 'slices' through the spots. The region of penumbral line formation does not show the Evershed outflow common in photospheric lines. The line intensity is a factor of two greater in sunspot penumbrae than in the photosphere, and at the limb the penumbral emission begins to depart from optical thinness, the line source function increasing with height. For a spot near disk center, the radial decrease in absolute magnetic field strength is steeper than the generally accepted dependence.
A Normalized Sunspot-Area Series Starting in 1832: an Update
Carrasco, V M S; Gallego, M C; Sánchez-Bajo, F
2016-01-01
A new normalized sunspot-area series has been reconstructed from the series obtained by the Royal Greenwich Observatory and other contemporary institutions for the period 1874 - 2008 and the area series compiled by De la Rue, Stewart, and Loewy from 1832 to 1868. Since the two sets of series do not overlap in time, we used as a link between them the new version of sunspot index number (Version 2) published by SILSO (Sunspot Index and Long-term Solar Observations). We also present a spectral analysis of the normalized area series in search of periodicities beyond the well-known solar cycle of 11 years and a study of the Waldmeier effect in the new version of sunspot-number and the sunspot-area series presented in this study. We conclude that while this effect is significant in the new series of sunspot number, it has a weak relationship with the sunspot-area series.
Borisov, A A; Bruevich, V V; Rozgacheva, I K; Shimanovskaya, E V
2015-01-01
We applied the method of continuous wavelet-transform to high-quality time-frequency analysis to the sets of observations of relative sunspot numbers. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi biennial up to the centennial period. These relatively low-frequency periodic variations of the solar activity gradually change the values of periods of different cycles in time. This phenomenon can be observed in every cycle of activity.
Origins of the Wolf Sunspot Number Series: Geomagnetic Underpinning
Cliver, E. W.; Svalgaard, L.
2007-12-01
The Wolf or International sunspot number (SSN) series is based on the work of Swiss astronomer Rudolf Wolf (1816-1893). Following the discovery of the sunspot cycle by Schwabe in 1843, Wolf culled sunspot counts from journals and observatory reports and combined them with his own observations to produce a SSN series that extended from 1700-1893. Thereafter the SSN record has been maintained by the Zurich Observatory and, since 1981, by the Royal Observatory of Belgium. The 1700-1893 SSN record constructed by Wolf has not been modified since his death. Here we show that Wolf's SSNs were not based solely on reports of sunspots but were calibrated by reference to geomagnetic range observations which closely track the sunspot number. Nor were these corrections small; for example Wolf multiplied the long series (1749-1796) of sunspot counts obtained by Staudacher by factors of 2.0 and 1.25, in turn, to obtain the numbers in use today. It is not surprising then that a competing SSN series obtained by Hoyt and Schatten based on group sunspot numbers is different, generally lower than that of Wolf. Comparison of the International number with current magnetic range observations indicates that, as Wolf found, the magnetic range (specifically, the average annual Y-component of mid-latitude stations) can be used as an independent check on the validity and stability of the SSN series. Moreover, the geomagnetic range series, which in itself is a long-term proxy of solar EUV emission, can be used to resolve discrepancies between the Wolf and Group SSN series during the 19th century.
Directional Time-Distance Probing of Model Sunspot Atmospheres
Moradi, H; Przybylski, D; Shelyag, S
2015-01-01
A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in the atmosphere, and then re-enter the interior to rejoin the seismic wave field normally confined there. In a series of recent numerical studies using translation invariant atmospheres, we utilised a "directional time-distance helioseismology" measurement scheme to study the implications of the returning fast and Alfv\\'en waves higher up in the solar atmosphere on the seismology at the photosphere (Cally & Moradi 2013; Moradi & Cally 2014). In this study, we extend our directional time-distance analysis to more realistic sunspot-like atmospheres to better understand the direct effects of the magnetic field on helioseismic travel-time measurements in sunspots. In line with our previous findings, we uncover a distinct frequency-dependant directional behaviour in the tra...
Gil-Alana, L.A.; Moreno, A; Pérez-de-Gracia, F. (Fernando)
2011-01-01
The last 20 years have witnessed a considerable increase in the use of time series techniques in econometrics. The articles in this important set have been chosen to illustrate the main themes in time series work as it relates to econometrics. The editor has written a new concise introduction to accompany the articles. Sections covered include: Ad Hoc Forecasting Procedures, ARIMA Modelling, Structural Time Series Models, Unit Roots, Detrending and Non-stationarity, Seasonality, Seasonal Adju...
Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times
Felipe, T; Crouch, A D; Birch, A C
2016-01-01
Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurfac...
Hurricanes in the Gulf of Mexico and the Caribbean Sea and their relationship with sunspots
Rojo-Garibaldi, Berenice; Salas-de-León, David Alberto; Sánchez, Norma Leticia; Monreal-Gómez, María Adela
2016-10-01
We present the results of a time series analysis of hurricanes and sunspots occurring from 1749 to 2010. Exploratory analysis shows that the total number of hurricanes is declining. This decline is related to an increase in sunspot activity. Spectral analysis shows a relationship between hurricane oscillation periods and sunspot activity. Several sunspot cycles were identified from the time series analysis.
Helioseismic Holography of Simulated Sunspots: Magnetic and Thermal Contributions to Travel Times
Felipe, T.; Braun, D. C.; Crouch, A. D.; Birch, A. C.
2016-10-01
Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path toward inversions for sunspot structure.
Time-variation of the near 5-month period of sunspot numbers
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The variation of the near 5-month period of sunspot numbers is discussed on the basis of the wavelet transform of the daily sunspot number series in the 14th-22nd solar cycles. The result shows that the period exists in every cycle and its energy density (amplitude) is comparatively large in the peak section of the cycle. In the distinct cycle, the length and intensity of the period is different, which means that the period varies with time. The near 25-day period is also analyzed and it is found to be time- variable and even not very stable in the peak section of the cycle. The variations of the two periods show that the near 5-month period should not be simply regarded as the multiples of the near 25-day period.
Time-Distance Helioseismology of Two Realistic Sunspot Simulations
DeGrave, K; Rempel, M
2014-01-01
Linear time-distance helioseismic inversions are carried out using several filtering schemes to determine vector flow velocities within two $\\sim100^2\\,{\\rm Mm^2}\\times 20\\,{\\rm Mm}$ realistic magnetohydrodynamic sunspot simulations of 25~hr. One simulation domain contains a model of a full sunspot (i.e. one with both an umbra and penumbra), while the other contains a pore (i.e. a spot without a penumbra). The goal is to test current helioseismic methods using these state-of-the-art simulations of magnetic structures. We find that horizontal flow correlations between inversion and simulation flow maps are reasonably high ($\\sim0.5$--0.8) in the upper 3~Mm at distances exceeding 25--30~Mm from spot center, but are substantially lower at smaller distances and larger depths. Inversions of forward-modeled travel times consistently outperform those of our measured travel times in terms of horizontal flow correlations, suggesting that our inability to recover flow structure near these active regions is largely due ...
Magnetic and Thermal Contributions to Helioseismic Travel times in Simulated Sunspots
Braun, Douglas; Felipe, Tobias; Birch, Aaron; Crouch, Ashley D.
2016-05-01
The interpretation of local helioseismic measurements of sunspots has long been a challenge, since waves propagating through sunspots are potentially affected by both mode conversion and changes in the thermal structure of the spots. We carry out numerical simulations of wave propagation through a variety of models which alternately isolate either the thermal or magnetic structure of the sunspot or include both of these. We find that helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. Using insight from ray theory, we find that travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level of the measurements) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it suggests a path towards inversions for sunspot structure. This research has been funded by the Spanish MINECO through grant AYA2014-55078-P, by the NASA Heliophysics Division through NNX14AD42G and NNH12CF23C, and the NSF Solar Terrestrial program through AGS-1127327.
Search for torsional oscillations in isolated sunspots
Griñón-Marín, A. B.; Socas-Navarro, H.; Centeno, R.
2017-07-01
In this work we seek evidence for global torsional oscillations in alpha sunspots. We have used long time series of continuum intensity and magnetic field vector maps from the Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) spacecraft. The time series analysed here span the total disk passage of 25 isolated sunspots. We found no evidence of global long-term periodic oscillations in the azimuthal angle of the sunspot magnetic field within 1 degree. This study could help us to understand the sunspot dynamics and its internal structure.
Galilei, Galileo; Reeves, Eileen; Helden, Albert van
2010-01-01
Galileo's telescopic discoveries, and especially his observation of sunspots, caused great debate in an age when the heavens were thought to be perfect and unchanging. Christoph Scheiner, a Jesuit mathematician, argued that sunspots were planets or moons crossing in front of the Sun. Galileo, on the other hand, countered that the spots were on or near the surface of the Sun itself, and he supported his position with a series of meticulous observations and mathematical demonstrations that eventually convinced even his rival. On Sunspots collects the correspondenc
Assessment of different sunspot number series using the cosmogenic isotope 44Ti in meteorites
Asvestari, Eleanna; Usoskin, Ilya G.; Kovaltsov, Gennady A.; Owens, Mathew J.; Krivova, Natalie A.; Rubinetti, Sara; Taricco, Carla
2017-01-01
Many sunspot number series exist suggesting different levels of solar activity during the past centuries. Their reliability can be assessed only by comparing them with alternative indirect proxies. We test different sunspot number series against the updated record of cosmogenic radionuclide 44Ti measured in meteorites. Two bounding scenarios of solar activity changes have been considered: the HH-scenario (based on the series by Svalgaard and Schatten, 2016) in particular predicting moderate activity during the Maunder minimum; and the LL-scenario (based on the RG series by Lockwood et al., 2014b) predicting moderate activity for the 18-19th centuries and the very low activity level for the Maunder minimum. For each scenario, the magnetic open solar flux, the heliospheric modulation potential and the expected production of 44Ti were computed. The calculated production rates were compared with the corresponding measurements of 44Ti activity in stony meteorites fallen since 1766. The analysis reveals that the LL-scenario is fully consistent with the measured 44Ti data, in particular recovering the observed secular trend between the 17th century and the Modern grand maximum. On the contrary, the HH-scenario appears significantly inconsistent with the data, mostly due the moderate level of activity during the Maunder minimum. It is concluded that the HH-scenario sunspot number reconstruction significantly overestimates solar activity prior to the mid-18th century, especially during the Maunder minimum. The exact level of solar activity after 1750 cannot be distinguished with this method, since both H- and L- scenarios appear statistically consistent with the data.
Time Series Forecasting: A Nonlinear Dynamics Approach
Sello, Stefano
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cy...
A New Calibrated Sunspot Group Series Since 1749: Statistics of Active Day Fractions
Usoskin, I G; Lockwood, M; Mursula, K; Owens, M; Solanki, S K
2015-01-01
Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [S_S] defined such that the observer is assumed to miss all of the groups with an area smaller than S_S and report all the groups larger than S_S. Next, using a Monte-Carlo method we construct, from the reference data set, a correction matrix for each observer. The correction matrices are significantly non-linear and cannot be approximate...
Wavelet analysis of sunspot relative numbers
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The time series of the monthly smoothed sunspot numbers in 1749-2000 is analyzed with the wavelet.The result shows that besides the known time-variation of the period about 11 years, other main periods of the sunspot numbers, such as the periods of about 100 years and so on,vary with time. We suggest that the time-variation of the main periods is the manifestation of the complex variation of sunspot numbers. It is significant to make a thorough study of the character and mechanism of the time-variation of the periods for proving prediction of sunspot numbers, especially for understanding the variation process of sunspot numbers.
On reconstruction of time series in climatology
Directory of Open Access Journals (Sweden)
V. Privalsky
2015-10-01
Full Text Available The approach to time series reconstruction in climatology based upon cross-correlation coefficients and regression equations is mathematically incorrect because it ignores the dependence of time series upon their past. The proper method described here for the bivariate case requires the autoregressive time- and frequency domains modeling of the time series which contains simultaneous observations of both scalar series with subsequent application of the model to restore the shorter one into the past. The method presents further development of previous efforts taken by a number of authors starting from A. Douglass who introduced some concepts of time series analysis into paleoclimatology. The method is applied to the monthly data of total solar irradiance (TSI, 1979–2014, and sunspot numbers (SSN, 1749–2014, to restore the TSI data over 1749–1978. The results of the reconstruction are in statistical agreement with observations.
Dependence of time derivative of horizontal geomagnetic field on sunspot number and aa index
National Research Council Canada - National Science Library
Falayi, Elijah O; Rabiu, Babatunde A
2013-01-01
This work investigated an interrelationship between the monthly means of time derivatives of horizontal geomagnetic field, dH/dt, sunspot number, R z , and aa index for the period of substorms (from −90 to −1800 nT...
Sunspot Sizes and the Solar Cycle: Analysis Using Kodaikanal White-light Digitized Data
Mandal, Sudip; Banerjee, Dipankar
2016-10-01
Sizes of the sunspots vary widely during the progression of a solar cycle. Long-term variation studies of different sunspot sizes are key to better understand the underlying process of sunspot formation and their connection to the solar dynamo. The Kodaikanal white-light digitized archive provides daily sunspot observations for a period of 90 years (1921-2011). Using different size criteria on the detected individual sunspots, we have generated yearly averaged sunspot area time series for the full Sun as well as for the individual hemispheres. In this Letter, we have used the sunspot area values instead of sunspot numbers used in earlier studies. Analysis of these different time series show that different properties of the sunspot cycles depend on the sunspot sizes. The “odd-even rule” double peaks during the cycle maxima and the long-term periodicities in the area data are found to be present for specific sunspot sizes and are absent or not so prominent in other size ranges. Apart from that, we also find a range of periodicities in the asymmetry index that have a dependency on the sunspot sizes. These statistical differences in the different size ranges may indicate that a complex dynamo action is responsible for the generation and dynamics of sunspots with different sizes.
2013-01-01
Time series analysis can be used to quantitatively monitor, describe, explain, and predict road safety developments. Time series analysis techniques offer the possibility of quantitatively modelling road safety developments in such a way that the dependencies between the observations of time series
Löhner-Böttcher, Johannes
2016-03-01
Context: The dynamic atmosphere of the Sun exhibits a wealth of magnetohydrodynamic (MHD) waves. In the presence of strong magnetic fields, most spectacular and powerful waves evolve in the sunspot atmosphere. Allover the sunspot area, continuously propagating waves generate strong oscillations in spectral intensity and velocity. The most prominent and fascinating phenomena are the 'umbral flashes' and 'running penumbral waves' as seen in the sunspot chromosphere. Their nature and relation have been under intense discussion in the last decades. Aims: Waves are suggested to propagate upward along the magnetic field lines of sunspots. An observational study is performed to prove or disprove the field-guided nature and coupling of the prevalent umbral and penumbral waves. Comprehensive spectroscopic observations at high resolution shall provide new insights into the wave characteristics and distribution across the sunspot atmosphere. Methods: Two prime sunspot observations were carried out with the Dunn Solar Telescope at the National Solar Observatory in New Mexico and with the Vacuum Tower Telescope at the Teide Observatory on Tenerife. The two-dimensional spectroscopic observations were performed with the interferometric spectrometers IBIS and TESOS. Multiple spectral lines are scanned co-temporally to sample the dynamics at the photospheric and chromospheric layers. The time series (1 - 2.5 h) taken at high spatial and temporal resolution are analyzed according to their evolution in spectral intensities and Doppler velocities. A wavelet analysis was used to obtain the wave power and dominating wave periods. A reconstruction of the magnetic field inclination based on sunspot oscillations was developed. Results and conclusions: Sunspot oscillations occur continuously in spectral intensity and velocity. The obtained wave characteristics of umbral flashes and running penumbral waves strongly support the scenario of slow-mode magnetoacoustic wave propagation along the
Are the sunspots really vanishing?
Directory of Open Access Journals (Sweden)
Clette Frédéric
2012-06-01
Full Text Available Context: The elapsed solar cycle (23 ended with an exceptionally long period of low activity and with unprecedented low levels for various series of solar irradiance and particle flux measurements. This unpredicted evolution of solar activity raised multiple questions about a future decline of the solar cycles and launched a quest for precursor signs of this possible deep solar transition over the last decade. Aim: We present here a review and overall interpretation of most current diagnostics of solar cycle 23, including the recent disagreements that appeared among solar reference indices and standard solar-based geo-indices, the indication of a changed pattern of internal torsional waves (helioseismology or the announced fading and magnetic weakening of sunspots. Methods: Based on a statistical analysis of detailed sunspot properties over the last 24 years, we complete the picture with new evidence of a strong global deficit of the smallest sunspots starting around 2000, in order to answer the question: are all sunspots about to disappear? Results: This global scale-dependent change in sunspot properties is confirmed to be real and not due to uncontrolled biases in some of the indices. It can also explain the recent discrepancies between solar indices by their different sensitivities to small and weak magnetic elements (small spots. The International Sunspot Index Ri, based on unweighted sunspot counts, proved to be particularly sensitive to this particular small-scale solar evolution. Conclusions: Our results and interpretation show the necessity to look backwards in time, more than 80 years ago. Indeed, the Sun seems to be actually returning to a past and hardly explored activity regime ending before the 1955–1995 Grand Maximum, which probably biased our current space-age view of solar activity.
DEFF Research Database (Denmark)
Moskowitz, Tobias J.; Ooi, Yao Hua; Heje Pedersen, Lasse
2012-01-01
under-reaction and delayed over-reaction. A diversified portfolio of time series momentum strategies across all asset classes delivers substantial abnormal returns with little exposure to standard asset pricing factors and performs best during extreme markets. Examining the trading activities...... of speculators and hedgers, we find that speculators profit from time series momentum at the expense of hedgers....
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2004-01-01
textabstractThis book considers periodic time series models for seasonal data, characterized by parameters that differ across the seasons, and focuses on their usefulness for out-of-sample forecasting. Providing an up-to-date survey of the recent developments in periodic time series, the book
Multivariate Time Series Decomposition into Oscillation Components.
Matsuda, Takeru; Komaki, Fumiyasu
2017-08-01
Many time series are considered to be a superposition of several oscillation components. We have proposed a method for decomposing univariate time series into oscillation components and estimating their phases (Matsuda & Komaki, 2017 ). In this study, we extend that method to multivariate time series. We assume that several oscillators underlie the given multivariate time series and that each variable corresponds to a superposition of the projections of the oscillators. Thus, the oscillators superpose on each variable with amplitude and phase modulation. Based on this idea, we develop gaussian linear state-space models and use them to decompose the given multivariate time series. The model parameters are estimated from data using the empirical Bayes method, and the number of oscillators is determined using the Akaike information criterion. Therefore, the proposed method extracts underlying oscillators in a data-driven manner and enables investigation of phase dynamics in a given multivariate time series. Numerical results show the effectiveness of the proposed method. From monthly mean north-south sunspot number data, the proposed method reveals an interesting phase relationship.
AAVSO Visual Sunspot Observations vs. SDO HMI Sunspot Catalog
Howe, R.
2014-06-01
(Abstract only) The most important issue with regard to using the SDO HMI data from the National Solar Observatory (NSO, http://www.nso.edu/staff/fwatson/STARA) is that their current model for creating sunspot counts does not split in groups and consequently does not provide a corresponding group count and Wolf number. As it is a different quantity, it cannot be mixed with the data from our sunspot networks. For the AAVSO with about seventy stations contributing each day, adding HMI sunspot data would anyway hardly change the resulting index. Perhaps, the best use of HMI data is for an external validation, by exploiting the fact that HMI provides a series that is rather close to the sunspot number and is acquired completely independently. So, it is unlikely to suffer from the same problems (jumps, biases) at the same time. This validation only works for rather short durations, as the lifetime of space instruments is limited and aging effects are often affecting the data over the mission. In addition, successive instruments have different properties: for example, the NSO model has not managed yet to reconcile the series from MDI and HMI. There is a ~10-15% jump. The first challenge that should be addressed by AAVSO using HMI data is the splitting in groups and deriving group properties. Then, together with the sunspot counts and areas per group, a lot more analyses and diagnostics can be derived (like the selective disappearance of the smallest sunspots?), that can help interpreting trends in the ratio SSN/other solar indices and many other solar effects.
Cross Recurrence Plots Analysis of the North-South Sunspot Activities
Ponyavin, Dmitri I.; Zolotova, Nadejda V.
A new technique of nonlinear interrelations between time series developed by Marwan & Kurths, (2002) has been applied to the sunspot data. By using this tools we have investigated synchronization and phase difference in annual sunspot areas -- time series available for Northern and Southern Hemispheres of the Sun.
Chaotic Time Series Forecasting Using Higher Order Neural Networks
Directory of Open Access Journals (Sweden)
Waddah Waheeb
2016-10-01
Full Text Available This study presents a novel application and comparison of higher order neural networks (HONNs to forecast benchmark chaotic time series. Two models of HONNs were implemented, namely functional link neural network (FLNN and pi-sigma neural network (PSNN. These models were tested on two benchmark time series; the monthly smoothed sunspot numbers and the Mackey-Glass time-delay differential equation time series. The forecasting performance of the HONNs is compared against the performance of different models previously used in the literature such as fuzzy and neural networks models. Simulation results showed that FLNN and PSNN offer good performance compared to many previously used hybrid models.
Schunker, Hannah; Cameron, Robert H; Birch, Aaron C
2013-01-01
In order to assess the ability of helioseismology to probe the subsurface structure and magnetic field of sunspots, we need to determine how helioseismic travel times depend on perturbations to sunspot models. Here we numerically simulate the propagation of f, p1, and p2 wave packets through magnetic sunspot models. Among the models we considered, a ~50 km change in the height of the Wilson depression and a change in the subsurface magnetic field geometry can both be detected above the observational noise level. We also find that the travel-time shifts due to changes in a sunspot model must be modeled by computing the effects of changing the reference sunspot model, and not by computing the effects of changing the subsurface structure in the quiet-Sun model. For p1 modes the latter is wrong by a factor of four. In conclusion, numerical modeling of MHD wave propagation is an essential tool for the interpretation of the effects of sunspots on seismic waveforms.
Sunspot Sizes and The Solar Cycle: Analysis Using Kodaikanal White-light Digitized Data
Mandal, Sudip
2016-01-01
Sizes of the sunspots vary in a wide range during the progression of a solar cycle. Long-term variation study of different sunspot sizes are key to better understand the underlying process of sunspot formation and their connection to the solar dynamo. Kodaikanal white-light digitized archive provides daily sunspot observations for a period of 90 years (1921-2011). Using different size criteria on the detected individual sunspots, we have generated yearly averaged sunspot area time series for the full Sun as well as for the individual hemispheres. In this paper, we have used the sunspot area values instead of sunspot numbers used in earlier studies. Analysis of these different time series show that different properties of the sunspot cycles depend on the sunspot sizes. The `odd-even rule', double peaks during the cycle maxima and the long-term periodicities in the area data are found to be present for specific sunspot sizes and are absent or not so prominent in other size ranges. Apart from that, we also find ...
Multivariate Time Series Search
National Aeronautics and Space Administration — Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical...
DEFF Research Database (Denmark)
Hisdal, H.; Holmqvist, E.; Hyvärinen, V.;
Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the......Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the...
DEFF Research Database (Denmark)
Hisdal, H.; Holmqvist, E.; Hyvärinen, V.
Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the......Awareness that emission of greenhouse gases will raise the global temperature and change the climate has led to studies trying to identify such changes in long-term climate and hydrologic time series. This report, written by the...
Self-affinity and nonextensivity of sunspots
Energy Technology Data Exchange (ETDEWEB)
Moret, M.A., E-mail: mamoret@gmail.com [Programa de Modelagem Computacional, SENAI, Cimatec, Av. Orlando Gomes, 1845, Piatã, 41650-010 Salvador, Bahia (Brazil); UNEB, Rua Silveira Martins, 2555, Cabula, 41150-000 Salvador, Bahia (Brazil)
2014-01-24
In this paper we study the time series of sunspots by using two different approaches, analyzing its self-affine behavior and studying its distribution. The long-range correlation exponent α has been calculated via Detrended Fluctuation Analysis and the power law vanishes to values greater than 11 years. On the other hand, the distribution of the sunspots obeys a q-exponential decay that suggests a non-extensive behavior. This observed characteristic seems to take an alternative interpretation of the sunspots dynamics. The present findings suggest us to propose a dynamic model of sunspots formation based on a nonlinear Fokker–Planck equation. Therefore its dynamic process follows the generalized thermostatistical formalism.
Acoustic absorption by sunspots
Braun, D. C.; Labonte, B. J.; Duvall, T. L., Jr.
1987-01-01
The paper presents the initial results of a series of observations designed to probe the nature of sunspots by detecting their influence on high-degree p-mode oscillations in the surrounding photosphere. The analysis decomposes the observed oscillations into radially propagating waves described by Hankel functions in a cylindrical coordinate system centered on the sunspot. From measurements of the differences in power between waves traveling outward and inward, it is demonstrated that sunspots appear to absorb as much as 50 percent of the incoming acoustic waves. It is found that for all three sunspots observed, the amount of absorption increases linearly with horizontal wavenumber. The effect is present in p-mode oscillations with wavelengths both significantly larger and smaller than the diameter of the sunspot umbrae. Actual absorption of acoustic energy of the magnitude observed may produce measurable decreases in the power and lifetimes of high-degree p-mode oscillations during periods of high solar activity.
Madsen, Henrik
2007-01-01
""In this book the author gives a detailed account of estimation, identification methodologies for univariate and multivariate stationary time-series models. The interesting aspect of this introductory book is that it contains several real data sets and the author made an effort to explain and motivate the methodology with real data. … this introductory book will be interesting and useful not only to undergraduate students in the UK universities but also to statisticians who are keen to learn time-series techniques and keen to apply them. I have no hesitation in recommending the book.""-Journa
Woodward, Wayne A; Elliott, Alan C
2011-01-01
""There is scarcely a standard technique that the reader will find left out … this book is highly recommended for those requiring a ready introduction to applicable methods in time series and serves as a useful resource for pedagogical purposes.""-International Statistical Review (2014), 82""Current time series theory for practice is well summarized in this book.""-Emmanuel Parzen, Texas A&M University""What an extraordinary range of topics covered, all very insightfully. I like [the authors'] innovations very much, such as the AR factor table.""-David Findley, U.S. Census Bureau (retired)""…
Time Distributions of Large and Small Sunspot Groups Over Four Solar Cycles
Kilcik, A; Abramenko, V; Goode, P R; Ozguc, A; Rozelot, J P; Cao, W; 10.1088/0004-637X/731/1/30
2011-01-01
Here we analyze solar activity by focusing on time variations of the number of sunspot groups (SGs) as a function of their modified Zurich class. We analyzed data for solar cycles 2023 by using Rome (cycles 2021) and Learmonth Solar Observatory (cycles 2223) SG numbers. All SGs recorded during these time intervals were separated into two groups. The first group includes small SGs (A, B, C, H, and J classes by Zurich classification) and the second group consists of large SGs (D, E, F, and G classes). We then calculated small and large SG numbers from their daily mean numbers as observed on the solar disk during a given month. We report that the time variations of small and large SG numbers are asymmetric except for the solar cycle 22. In general large SG numbers appear to reach their maximum in the middle of the solar cycle (phase 0.450.5), while the international sunspot numbers and the small SG numbers generally peak much earlier (solar cycle phase 0.290.35). Moreover, the 10.7 cm solar radio flux, the facul...
DEFF Research Database (Denmark)
Fischer, Paul; Hilbert, Astrid
2012-01-01
commands, our application is select-and-click-driven. It allows to derive many different sequences of deviations for a given time series and to visualize them in different ways in order to judge their expressive power and to reuse the procedure found. For many transformations or model-ts, the user may...
Clette, Frédéric; Vaquero, José M; Cliver, Edward W
2014-01-01
Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (1998a,b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the sunspot number calibration. While the early part of the sunspot record befor...
Sliced Inverse Regression for Time Series Analysis
Chen, Li-Sue
1995-11-01
In this thesis, general nonlinear models for time series data are considered. A basic form is x _{t} = f(beta_sp{1} {T}X_{t-1},beta_sp {2}{T}X_{t-1},... , beta_sp{k}{T}X_ {t-1},varepsilon_{t}), where x_{t} is an observed time series data, X_{t } is the first d time lag vector, (x _{t},x_{t-1},... ,x _{t-d-1}), f is an unknown function, beta_{i}'s are unknown vectors, varepsilon_{t }'s are independent distributed. Special cases include AR and TAR models. We investigate the feasibility applying SIR/PHD (Li 1990, 1991) (the sliced inverse regression and principal Hessian methods) in estimating beta _{i}'s. PCA (Principal component analysis) is brought in to check one critical condition for SIR/PHD. Through simulation and a study on 3 well -known data sets of Canadian lynx, U.S. unemployment rate and sunspot numbers, we demonstrate how SIR/PHD can effectively retrieve the interesting low-dimension structures for time series data.
Liang, X San
2014-01-01
Given two time series, can one tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion namely information flow, we arrive at a concise formula and give this challenging question, which is of wide concern in different disciplines, a positive answer. Here causality is measured by the time rate of change of information flowing from one series, say, X2, to another, X1. The measure is asymmetric between the two parties and, particularly, if the process underlying X1 does not depend on X2, then the resulting causality from X2 to X1 vanishes. The formula is tight in form, involving only the commonly used statistics, sample covariances. It has been validated with touchstone series purportedly generated with one-way causality. It has also been applied to the investigation of real world problems; an example presented here is the cause-effect relation between two climate modes, El Ni\\~no and Indian Ocean Dipole, which have been linked to the hazards in f...
Time Series Forecasting A Nonlinear Dynamics Approach
Sello, S
1999-01-01
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space,Lyapunov spectrum,chaotic behaviour. The model is based on a locally hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous paramet...
Introduction to Time Series Modeling
Kitagawa, Genshiro
2010-01-01
In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to learn fundamental methods of time series modeling. Illustrating how to build models for time series using basic methods, "Introduction to Time Series Modeling" covers numerous time series models and the various tools f
Directory of Open Access Journals (Sweden)
Milos Miljanovic
2012-02-01
Full Text Available The purpose of this paper is to perform evaluation of two different neural network architectures used for solving temporal problems, i.e. time series prediction. The data sets in this project include Mackey-Glass,Sunspots, and Standard & Poor's 500, the stock market index. The study also presents a comparison study on the two networks and their performance.
Sych, Robert
2015-01-01
The review addresses the spatial frequency morphology of sources of sunspot oscillations and waves, including their localization, size, oscillation periods, height localization with the mechanism of cut-off frequency that forms the observed emission variability. Dynamic of sunspot wave processes, provides the information about the structure of wave fronts and their time variations, investigates the oscillation frequency transformation depending on the wave energy is shown. The initializing solar flares caused by trigger agents like magnetoacoustic waves, accelerated particle beams, and shocks are discussed. Special attention is paid to the relation between the flare reconnection periodic initialization and the dynamics of sunspot slow magnetoacoustic waves. A short review of theoretical models of sunspot oscillations is provided.
GPS Position Time Series @ JPL
Owen, Susan; Moore, Angelyn; Kedar, Sharon; Liu, Zhen; Webb, Frank; Heflin, Mike; Desai, Shailen
2013-01-01
Different flavors of GPS time series analysis at JPL - Use same GPS Precise Point Positioning Analysis raw time series - Variations in time series analysis/post-processing driven by different users. center dot JPL Global Time Series/Velocities - researchers studying reference frame, combining with VLBI/SLR/DORIS center dot JPL/SOPAC Combined Time Series/Velocities - crustal deformation for tectonic, volcanic, ground water studies center dot ARIA Time Series/Coseismic Data Products - Hazard monitoring and response focused center dot ARIA data system designed to integrate GPS and InSAR - GPS tropospheric delay used for correcting InSAR - Caltech's GIANT time series analysis uses GPS to correct orbital errors in InSAR - Zhen Liu's talking tomorrow on InSAR Time Series analysis
GPS Position Time Series @ JPL
Owen, Susan; Moore, Angelyn; Kedar, Sharon; Liu, Zhen; Webb, Frank; Heflin, Mike; Desai, Shailen
2013-01-01
Different flavors of GPS time series analysis at JPL - Use same GPS Precise Point Positioning Analysis raw time series - Variations in time series analysis/post-processing driven by different users. center dot JPL Global Time Series/Velocities - researchers studying reference frame, combining with VLBI/SLR/DORIS center dot JPL/SOPAC Combined Time Series/Velocities - crustal deformation for tectonic, volcanic, ground water studies center dot ARIA Time Series/Coseismic Data Products - Hazard monitoring and response focused center dot ARIA data system designed to integrate GPS and InSAR - GPS tropospheric delay used for correcting InSAR - Caltech's GIANT time series analysis uses GPS to correct orbital errors in InSAR - Zhen Liu's talking tomorrow on InSAR Time Series analysis
Felipe, T.; Braun, D. C.; Birch, A. C.
2017-08-01
Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods.
Time series analysis by the Maximum Entropy method
Energy Technology Data Exchange (ETDEWEB)
Kirk, B.L.; Rust, B.W.; Van Winkle, W.
1979-01-01
The principal subject of this report is the use of the Maximum Entropy method for spectral analysis of time series. The classical Fourier method is also discussed, mainly as a standard for comparison with the Maximum Entropy method. Examples are given which clearly demonstrate the superiority of the latter method over the former when the time series is short. The report also includes a chapter outlining the theory of the method, a discussion of the effects of noise in the data, a chapter on significance tests, a discussion of the problem of choosing the prediction filter length, and, most importantly, a description of a package of FORTRAN subroutines for making the various calculations. Cross-referenced program listings are given in the appendices. The report also includes a chapter demonstrating the use of the programs by means of an example. Real time series like the lynx data and sunspot numbers are also analyzed. 22 figures, 21 tables, 53 references.
Short Periodicities in Latitudinal Variation of Sunspots
Kim, Bang-Yeop; Chang, Heon-Young
2011-06-01
The latitudinal variation of sunspots appearing during the period from 1874 to 2009 has been studied in terms of centerof- latitude (COL). The butterfly diagram has been used to study the evolution of the magnetic field and the dynamics at the bottom of the solar convection zone. Short-term periodicities have been of particular interest, in that they are somehow related to the structure and dynamics of the solar interior. We thus have focused our investigation on shortterm periodicities. We first calculated COL by averaging the latitude of sunspots with the weight function in area. Then, we analyzed the time series of COL using the wavelet transform technique. We found that a periodicity of ~5 years is the most dominant feature in the time series of COL, with the exception of the ~11 year solar cycle itself. This periodicity can be easily understood by considering small humps between the minima in the area-weighted butterfly diagram. However, we find that periodicities of ~1.3 (0.064), ~1.5 (0.056), or ~1.8 (0.046) years ( 1/ month ), which have been previously suggested as evidence of links between the changing structure of the sunspot zone and the tachocline rotation rate oscillations, are insignificant and inconsistent. We therefore conclude that the only existing short-term periodicity is of ~5 years, and that periodicities of ~1.3, ~1.5, or ~1.8 years are likely to be artifacts due to random noise of small sunspots.
Kobanov, Nikolai; Kustov, Arseniy; Chupin, Sergey; Chelpanov, Andrey; 10.1007/s11207-013-0247-2
2013-01-01
We present an investigation of line-of-sight (LOS) velocity oscillations in solar faculae and sunspots. To study the phase relations between chromosphere and photosphere oscillations of the LOS velocity, we measured the time lag of the chromospheric signal relative to the photospheric one for several faculae and sunspots in a set of spectral line pairs. The measured time lags are different for different objects. The mean measured delay between the oscillations in the five-minute band in faculae is 50s for the SiI 10827{\\AA}-HeI 10830{\\AA} pair; for the pair FeI 6569{\\AA}-H-alpha 6563{\\AA} the mean delay is 20s; for the pair FeI 4551{\\AA}-BaII 4554{\\AA} the mean delay is 7s; for the pair SiI 8536{\\AA}-CaII 8542{\\AA} the mean delay is 20s. For the oscillations in the three-minute band in sunspot umbrae the mean delay is 55s for the SiI 10827{\\AA}-HeI 10830{\\AA} pair; for the Fe I 6569{\\AA}-H-alpha 6563{\\AA} pair it was not possible to determine the delay; for the FeI 4551{\\AA}-BaII 4554{\\AA} pair the mean delay...
The revised Brussels-Locarno Sunspot Number (1981-2015)
Clette, Frédéric; Cagnotti, Marco; Cortesi, Sergio; Bulling, Andreas
2015-01-01
In 1981, the production of the international Sunspot Number moved from the Z\\"{u}rich Observatory to the Royal Observatory of Belgium, marking a very important transition in the history of the Sunspot Number. Those recent decades are particularly important for linking recent modern solar indices and fluxes and the past Sunspot Number series. However, large variations have been recently identified in the scale of the Sunspot Number between 1981 and the present. Here, we reconstruct a new average Sunspot Number series $S_N$ using long-duration stations between 1981 and 2015. We also extend this reconstruction using long-time series from 35 stations over 1945-2015, which includes the 1981 transition. In both reconstructions, we also derive a parallel Group Number series $G_N$. Our results confirm the variable trends of the Locarno pilot station. We also verify the scale of the resulting 1981-2015 correction factor relative to the preceding period 1945--1980. By comparing the new $S_N$ and $G_N$ series, we find t...
The Revised Brussels-Locarno Sunspot Number (1981 - 2015)
Clette, Frédéric; Lefèvre, Laure; Cagnotti, Marco; Cortesi, Sergio; Bulling, Andreas
2016-04-01
In 1981, the production of the international sunspot number moved from the Zürich Observatory to the Royal Observatory of Belgium, with a new pilot station: the Specola Solare Ticinese Observatory in Locarno, Switzerland. This marked a profound transition in the history of the sunspot number. Those recent decades are particularly important as they provide the link between recent modern solar indices and the entire sunspot-number series extending back to the eighteenth century. However, large variations have recently been identified in the scale of the sunspot number during this recent time period. Here, we refine the determination of those recent inhomogeneities by reconstructing a new average sunspot-number series [ SN] from a subset of long-duration stations between 1981 and 2015. We also extend this reconstruction by gathering long time series from 35 stations over 1945 - 2015, thus straddling the critical 1981 transition. In both reconstructions, we also derive a parallel group number series [ GN] built by the same method from exactly the same data set. Our results confirm the variable trends associated with drifts of the Locarno pilot station, which start only in 1983. They lead to a fully uniform SN-series over the entire 1945 - 2015 interval. By comparing the new SN- and GN-series, we find that a constant quadratic relation exists between those two indices over Cycles 19 to 23. Comparisons with a few other solar indices additionally validate this and reveal some possible undetected problems in those series. Using this new reference SN, we find that observing stations are surprisingly grouped among distinct subsets that share similar personal k-scaling coefficients. These various results also open the way to implementing a more advanced method for producing the sunspot number in the future.
The Revised Brussels-Locarno Sunspot Number (1981 - 2015)
Clette, Frédéric; Lefèvre, Laure; Cagnotti, Marco; Cortesi, Sergio; Bulling, Andreas
2016-11-01
In 1981, the production of the international sunspot number moved from the Zürich Observatory to the Royal Observatory of Belgium, with a new pilot station: the Specola Solare Ticinese Observatory in Locarno, Switzerland. This marked a profound transition in the history of the sunspot number. Those recent decades are particularly important as they provide the link between recent modern solar indices and the entire sunspot-number series extending back to the eighteenth century. However, large variations have recently been identified in the scale of the sunspot number during this recent time period. Here, we refine the determination of those recent inhomogeneities by reconstructing a new average sunspot-number series [SN] from a subset of long-duration stations between 1981 and 2015. We also extend this reconstruction by gathering long time series from 35 stations over 1945 - 2015, thus straddling the critical 1981 transition. In both reconstructions, we also derive a parallel group number series [GN] built by the same method from exactly the same data set. Our results confirm the variable trends associated with drifts of the Locarno pilot station, which start only in 1983. They lead to a fully uniform SN-series over the entire 1945 - 2015 interval. By comparing the new SN- and GN-series, we find that a constant quadratic relation exists between those two indices over Cycles 19 to 23. Comparisons with a few other solar indices additionally validate this and reveal some possible undetected problems in those series. Using this new reference SN, we find that observing stations are surprisingly grouped among distinct subsets that share similar personal k-scaling coefficients. These various results also open the way to implementing a more advanced method for producing the sunspot number in the future.
Predicting Nonlinear Time Series
1993-12-01
response becomes R,(k) = f (Y FV,(k)) (2.4) where Wy specifies the weight associated with the output of node i to the input of nodej in the next layer and...interconnections for each of these previous nodes. 18 prr~~~o• wfe :t iam i -- ---- --- --- --- Figure 5: Delay block for ATNN [9] Thus, nodej receives the...computed values, aj(tn), and dj(tn) denotes the desired output of nodej at time in. In this thesis, the weights and time delays update after each input
Advances in time series forecasting
Cagdas, Hakan Aladag
2012-01-01
Readers will learn how these methods work and how these approaches can be used to forecast real life time series. The hybrid forecasting model is also explained. Data presented in this e-book is problem based and is taken from real life situations. It is a valuable resource for students, statisticians and working professionals interested in advanced time series analysis.
Comments on nonparametric predictions of sunspot numbers
DEFF Research Database (Denmark)
Jensen, J.L.
1993-01-01
Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed.......Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed....
Time Series with Tailored Nonlinearities
Raeth, C
2015-01-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncor- related Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for e.g. turbulence and financial data can thus be explained in terms of phase correlations.
Fractal and Multifractal Time Series
Kantelhardt, Jan W
2008-01-01
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude, allowing for a characterisation of the data and the generating complex system by fractal (or multifractal) scaling exponents. In addition, fractal and multifractal approaches can be used for modelling time series and deriving predictions regarding extreme events. This review article describes and exemplifies several methods originating from Statistical Physics and Applied Mathematics, which have been used for fractal and multifractal time series analysis.
Models for dependent time series
Tunnicliffe Wilson, Granville; Haywood, John
2015-01-01
Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data.The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational mater
Time series prediction in agroecosystems
Cortina-Januchs, M. G.; Quintanilla-Dominguez, J.; Vega-Corona, A.; Andina, D.
2012-04-01
This work proposes a novel model to predict time series such as frost, precipitation, temperature, solar radiation, all of them important variables for the agriculture process. In the proposed model, Artificial Neural Networks (ANN) combined with clustering algorithms and sensor data fusion are used. The real time series are obtained from different sensors. The clustering algorithms find relationships between variables, clustering involves the task of dividing data sets, which assigns the same label to members who belong to the same group, so that each group is homogeneous and distinct from the others. Those relationships provide information to the ANN in order to obtain the time series prediction. The most important issue of ANN in time series prediction is generalization, which refers to their ability to produce reasonable predictions on data sets other than those used for the estimation of the model parameters.
Time series analysis time series analysis methods and applications
Rao, Tata Subba; Rao, C R
2012-01-01
The field of statistics not only affects all areas of scientific activity, but also many other matters such as public policy. It is branching rapidly into so many different subjects that a series of handbooks is the only way of comprehensively presenting the various aspects of statistical methodology, applications, and recent developments. The Handbook of Statistics is a series of self-contained reference books. Each volume is devoted to a particular topic in statistics, with Volume 30 dealing with time series. The series is addressed to the entire community of statisticians and scientists in various disciplines who use statistical methodology in their work. At the same time, special emphasis is placed on applications-oriented techniques, with the applied statistician in mind as the primary audience. Comprehensively presents the various aspects of statistical methodology Discusses a wide variety of diverse applications and recent developments Contributors are internationally renowened experts in their respect...
Detecting and interpreting distortions in hierarchical organization of complex time series
Drożdż, Stanisław
2015-01-01
Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using the selected time series representing such diverse phenomena like price changes and inter-transaction times in the financial markets, sentence length variability in the narrative texts, Missouri River discharge and Sunspot Number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left-sided but in some cases also right-sided. We present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying composition of the time series. One particularly intriguing case of this later kind of asymmetry is detected in the daily reported Sunspot Number variability. This signals that either the commonly used famous Wolf formula distorts the real d...
Characterizing time series via complexity-entropy curves
Ribeiro, Haroldo V.; Jauregui, Max; Zunino, Luciano; Lenzi, Ervin K.
2017-06-01
The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q -complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.
Benchmarking of energy time series
Energy Technology Data Exchange (ETDEWEB)
Williamson, M.A.
1990-04-01
Benchmarking consists of the adjustment of time series data from one source in order to achieve agreement with similar data from a second source. The data from the latter source are referred to as the benchmark(s), and often differ in that they are observed at a lower frequency, represent a higher level of temporal aggregation, and/or are considered to be of greater accuracy. This report provides an extensive survey of benchmarking procedures which have appeared in the statistical literature, and reviews specific benchmarking procedures currently used by the Energy Information Administration (EIA). The literature survey includes a technical summary of the major benchmarking methods and their statistical properties. Factors influencing the choice and application of particular techniques are described and the impact of benchmark accuracy is discussed. EIA applications and procedures are reviewed and evaluated for residential natural gas deliveries series and coal production series. It is found that the current method of adjusting the natural gas series is consistent with the behavior of the series and the methods used in obtaining the initial data. As a result, no change is recommended. For the coal production series, a staged approach based on a first differencing technique is recommended over the current procedure. A comparison of the adjustments produced by the two methods is made for the 1987 Indiana coal production series. 32 refs., 5 figs., 1 tab.
Random time series in Astronomy
Vaughan, Simon
2013-01-01
Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle, and over time (usually called light curves by astronomers). In the time domain we see transient events such as supernovae, gamma-ray bursts, and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars, and pulsations of stars in nearby galaxies; and persistent aperiodic variations (`noise') from powerful systems like accreting black holes. I review just a few of the recent and future challenges in the burgeoning area of Time Domain Astrophysics, with particular attention to persistently variable sources, the recovery of reliable noise power spectra from sparsely sampled time series, higher-order properties of accreting black holes, and time delays and correlations in multivariate time series.
Random time series in astronomy.
Vaughan, Simon
2013-02-13
Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle and over time (usually called light curves by astronomers). In the time domain, we see transient events such as supernovae, gamma-ray bursts and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars and pulsations of stars in nearby galaxies; and we see persistent aperiodic variations ('noise') from powerful systems such as accreting black holes. I review just a few of the recent and future challenges in the burgeoning area of time domain astrophysics, with particular attention to persistently variable sources, the recovery of reliable noise power spectra from sparsely sampled time series, higher order properties of accreting black holes, and time delays and correlations in multi-variate time series.
Signatures of running penumbral waves in sunspot photospheres
Löhner-Böttcher, Johannes
2015-01-01
The highly dynamic atmosphere above sunspots exhibits a wealth of magnetohydrodynamic (MHD) waves. Recent studies suggest a coupled nature of the most prominent phenomena: umbral flashes (UFs) and running penumbral waves (RPWs). From an observational point of view, we perform a height-dependent study of RPWs, compare their wave characteristics and aim to track down these so far only chromospherically observed phenomena to photospheric layers to prove the upward propagating field-guided nature of RPWs. We analyze a time series (58\\,min) of multi-wavelength observations of an isolated circular sunspot (NOAA11823) taken at high spatial and temporal resolution in spectroscopic mode with the Interferometric BIdimensional Spectro-polarimeter (IBIS/DST). By means of a multi-layer intensity sampling, velocity comparisons, wavelet power analysis and sectorial studies of time-slices, we retrieve the power distribution, characteristic periodicities and propagation characteristics of sunspot waves at photospheric and chr...
Sunspot Catalogue of the Valencia Observatory (1920-1928)
Carrasco, V M S; Aparicio, A J P; Gallego, M C
2014-01-01
A sunspot catalogue was maintained by the Astronomical Observatory of Valencia University (Spain) from 1920 to 1928. Here we present a machine-readable version of this catalogue (OV catalog or OVc), including a quality control analysis. Sunspot number (total and hemispheric) and sunspot area series are constructed using this catalogue. The OV catalog's data are compared with other available solar data, demonstrating that the present contribution provides the scientific community with a reliable catalogue of sunspot data.
The new Sunspot Number: assembling all corrections
Frédéric,; Lefèvre, Laure
2015-01-01
The Sunspot Number, created by R.Wolf in 1849, provides a direct long-term record of solar activity from 1700 to the present. In spite of its central role in multiple studies of the solar dynamo and of the past Sun-Earth relations, it was never submitted to a global critical revision. However, various discrepancies with other solar indices recently motivated a full re-calibration of this series. Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described in Clette et al. 2014, we assembled all corrections in order to produce a new standard version of this reference time series. In this paper, we explain the three main corrections and the criteria used to choose a final optimal version of each correction factor or function, given the available information and published analyses. We then discuss the good agreement obtained with the Group sunspot Number derived from a recent reconstruction. Among the implications emerging from this re-calibrated ser...
Numerical simulations of the subsurface structure of sunspots
Rempel, M.; Cheung, M.; Birch, A. C.; Braun, D. C.
2011-12-01
Knowledge of the subsurface magnetic field and flow structure of sunspots is essential for understanding the processes involved in their formation, dynamic evolution and decay. Information on the subsurface structure can be obtained by either direct numerical modeling or helioseismic inversions. Numerical simulations have reached only in recent years the point at which entire sunspots or even active regions can be modeled including all relevant physical processes such as 3D radiative transfer and a realistic equation of state. We present in this talk results from a series of different models: from simulations of individual sunspots (with and without penumbrae) in differently sized computational domains to simulations of the active region formation process (flux emergence). It is found in all models that the subsurface magnetic field fragments on an intermediate scale (larger than the scale of sunspot fine structure such as umbral dots); most of these fragmentations become visible as light bridges or flux separation events in the photosphere. The subsurface field strength is found to be in the 5-10 kG range. The simulated sunspots are surrounded by large scale flows, the most dominant and robust flow component is a deep reaching outflow with an amplitude reaching about 50% of the convective RMS velocity at the respective depth. The simulated sunspots show helioseismic signatures (frequency dependent travel time shifts) similar to those in observed sunspots. On the other hand it is clear from the simulations that these signatures originate in the upper most 2-3 Mm of the convection zone, since only there substantial perturbations of the wave speed are present. The contributions from deeper layers are insignificant, in particular a direct comparison between an 8 Mm and 16 Mm deep simulation leads to indiscernible helioseismic differences. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work is in part supported
Sunspot Rotation as a Driver of Major Solar Eruptions in NOAA Active Region 12158
Vemareddy, P; Ravindra, B
2016-01-01
We studied the developing conditions of sigmoid structure under the influence of magnetic non-potential characteristics of a rotating sunspot in the active region (AR) 12158. Vector magnetic field measurements from Helioseismic Magnetic Imager and coronal EUV observations from Atmospheric Imaging Assembly reveal that the erupting inverse-S sigmoid had roots in the location of the rotating sunspot. Sunspot rotates at a rate of 0-5deg/h with increasing trend in the first half followed by a decrease. Time evolution of many non-potential parameters had a well correspondence with the sunspot rotation. The evolution of the AR magnetic structure is approximated by a time series of force free equilibria. The NLFFF magnetic structure around the sunspot manifests the observed sigmoid structure. Field lines from the sunspot periphery constitute the body of the sigmoid and those from interior overly the sigmoid similar to a fluxrope structure. While the sunspot is being rotating, two major CME eruptions occurred in the A...
Detecting and interpreting distortions in hierarchical organization of complex time series
DroŻdŻ, Stanisław; OświÈ©cimka, Paweł
2015-03-01
Hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept. For model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric. Using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets, sentence length variability in narrative texts, Missouri River discharge, and sunspot number variability as examples, we show that the resulting singularity spectra appear strongly asymmetric, more often left sided but in some cases also right sided. We present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying the composition of the time series. One particularly intriguing case of this latter kind of asymmetry is detected in the daily reported sunspot number variability. This signals that either the commonly used famous Wolf formula distorts the real dynamics in expressing the largest sunspot numbers or, if not, that their dynamics is governed by a somewhat different mechanism.
SHAPE-BASED TIME SERIES SIMILARITY MEASURE AND PATTERN DISCOVERY ALGORITHM
Institute of Scientific and Technical Information of China (English)
Zeng Fanzi; Qiu Zhengding; Li Dongsheng; Yue Jianhai
2005-01-01
Pattern discovery from time series is of fundamental importance. Most of the algorithms of pattern discovery in time series capture the values of time series based on some kinds of similarity measures. Affected by the scale and baseline, value-based methods bring about problem when the objective is to capture the shape. Thus, a similarity measure based on shape, Sh measure, is originally proposed, andthe properties of this similarity and corresponding proofs are given. Then a time series shape pattern discovery algorithm based on Sh measure is put forward. The proposed algorithm is terminated in finite iteration with given computational and storage complexity. Finally the experiments on synthetic datasets and sunspot datasets demonstrate that the time series shape pattern algorithm is valid.
The Impact of the Revised Sunspot Record on Solar Irradiance Reconstructions
Kopp, G; Lean, J; Wu, C J
2016-01-01
Reliable historical records of total solar irradiance (TSI) are needed for climate change attribution and research to assess the extent to which long-term variations in the Sun's radiant energy incident on the Earth may exacerbate (or mitigate) the more dominant warming in recent centuries due to increasing concentrations of greenhouse gases. We investigate potential impacts of the new Sunspot Index and Long-term Solar Observations (SILSO) sunspot-number time series on model reconstructions of TSI. In contemporary TSI records, variations on time scales longer than about a day are dominated by the opposing effects of sunspot darkening and facular brightening. These two surface magnetic features, retrieved either from direct observations or from solar activity proxies, are combined in TSI models to reproduce the current TSI observational record. Indices that manifest solar-surface magnetic activity, in particular the sunspot-number record, then enable the reconstruction of historical TSI. Revisions to the sunsp...
Long-Term Sunspot Number Prediction based on EMD Analysis and AR Model
Institute of Scientific and Technical Information of China (English)
Tong Xu; Jian Wu; Zhen-Sen Wu; Qiang Li
2008-01-01
The Empirical Mode Decomposition (EMD) and Auto-Regressive model (AR) are applied to a long-term prediction of sunspot numbers. With the sample data of sunspot numbers from 1848 to 1992, the method is evaluated by examining the measured data of the solar cycle 23 with the prediction: different time scale components are obtained by the EMD method and multi-step predicted values are combined to reconstruct the sunspot number time series. The result is remarkably good in comparison to the predictions made by the solar dynamo and precursor approaches for cycle 23. Sunspot numbers of the coming solar cycle 24 are obtained with the data from 1848 to 2007, the maximum amplitude of the next solar cycle is predicted to be about 112 in 2011-2012.
An alternative measure of solar activity from detailed sunspot datasets
Muraközy, Judit; Ludmány, András
2016-01-01
The sunspot number is analyzed by using detailed sunspot data, including aspects of observability, sunspot sizes, and proper identification of sunspot groups as discrete entities of the solar activity. The tests show that besides the subjective factors there are also objective causes of the ambiguities in the series of sunspot numbers. To introduce an alternative activity measure the physical meaning of the sunspot number has to be reconsidered. It contains two components whose numbers are governed by different physical mechanisms, this is one source of the ambiguity. This article suggests an activity index, which is the amount of emerged magnetic flux. The only long-term proxy measure is the detailed sunspot area dataset with proper calibration to the magnetic flux amount. The Debrecen sunspot databases provide an appropriate source for the establishment of the suggested activity index.
Properties of a Decaying Sunspot
Balthasar, H; Gömöry, P; Muglach, K; Puschmann, K G; Shimizu, T; Verma, M
2013-01-01
A small decaying sunspot was observed with the Vacuum Tower Telescope (VTT) on Tenerife and the Japanese Hinode satellite. We obtained full Stokes scans in several wavelengths covering different heights in the solar atmosphere. Imaging time series from Hinode and the Solar Dynamics Observatory (SDO) complete our data sets. The spot is surrounded by a moat flow, which persists also on that side of the spot where the penumbra already had disappeared. Close to the spot, we find a chromospheric location with downflows of more than 10 km/s without photospheric counterpart. The height dependence of the vertical component of the magnetic field strength is determined in two different ways that yielded different results in previous investigations. Such a difference still exists in our present data, but it is not as pronounced as in the past.
A Time Series Forecasting Method
Directory of Open Access Journals (Sweden)
Wang Zhao-Yu
2017-01-01
Full Text Available This paper proposes a novel time series forecasting method based on a weighted self-constructing clustering technique. The weighted self-constructing clustering processes all the data patterns incrementally. If a data pattern is not similar enough to an existing cluster, it forms a new cluster of its own. However, if a data pattern is similar enough to an existing cluster, it is removed from the cluster it currently belongs to and added to the most similar cluster. During the clustering process, weights are learned for each cluster. Given a series of time-stamped data up to time t, we divide it into a set of training patterns. By using the weighted self-constructing clustering, the training patterns are grouped into a set of clusters. To estimate the value at time t + 1, we find the k nearest neighbors of the input pattern and use these k neighbors to decide the estimation. Experimental results are shown to demonstrate the effectiveness of the proposed approach.
International Work-Conference on Time Series
Pomares, Héctor; Valenzuela, Olga
2017-01-01
This volume of selected and peer-reviewed contributions on the latest developments in time series analysis and forecasting updates the reader on topics such as analysis of irregularly sampled time series, multi-scale analysis of univariate and multivariate time series, linear and non-linear time series models, advanced time series forecasting methods, applications in time series analysis and forecasting, advanced methods and online learning in time series and high-dimensional and complex/big data time series. The contributions were originally presented at the International Work-Conference on Time Series, ITISE 2016, held in Granada, Spain, June 27-29, 2016. The series of ITISE conferences provides a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary rese arch encompassing the disciplines of comput...
Event Discovery in Time Series
Preston, Dan; Brodley, Carla
2009-01-01
The discovery of events in time series can have important implications, such as identifying microlensing events in astronomical surveys, or changes in a patient's electrocardiogram. Current methods for identifying events require a sliding window of a fixed size, which is not ideal for all applications and could overlook important events. In this work, we develop probability models for calculating the significance of an arbitrary-sized sliding window and use these probabilities to find areas of significance. Because a brute force search of all sliding windows and all window sizes would be computationally intractable, we introduce a method for quickly approximating the results. We apply our method to over 100,000 astronomical time series from the MACHO survey, in which 56 different sections of the sky are considered, each with one or more known events. Our method was able to recover 100% of these events in the top 1% of the results, essentially pruning 99% of the data. Interestingly, our method was able to iden...
Low Dimensional Chaos from the Group Sunspot Numbers
Institute of Scientific and Technical Information of China (English)
Qi-Xiu Li; Ke-Jun Li
2007-01-01
We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor.This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers.We estimate the maximal Lyaponuv exponent (MLE) for the Rg series to be positive and to equal approximately 0.0187±0.0023 (month-1).Thus,the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46±0.5 years.which is slightly different with the predictability time obtained from Rz.However,they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.
Detecting chaos from time series
Xiaofeng, Gong; Lai, C. H.
2000-02-01
In this paper, an entirely data-based method to detect chaos from the time series is developed by introducing icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points (the p -steps icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> -neighbour points). We demonstrate that for deterministic chaotic systems, there exists a linear relationship between the logarithm of the average number of icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> p -neighbour points, lnn p ,icons/Journals/Common/epsilon" ALT="epsilon" ALIGN="TOP"/> , and the time step, p . The coefficient can be related to the KS entropy of the system. The effects of the embedding dimension and noise are also discussed.
Helioseismology of a Realistic Magnetoconvective Sunspot Simulation
Braun, D. C.; Birch, A. C.; Rempel, M.; Duvall, T. L., Jr.
2012-01-01
We compare helioseismic travel-time shifts measured from a realistic magnetoconvective sunspot simulation using both helioseismic holography and time-distance helioseismology, and measured from real sunspots observed with the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory and the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory. We find remarkable similarities in the travel-time shifts measured between the methodologies applied and between the simulated and real sunspots. Forward modeling of the travel-time shifts using either Born or ray approximation kernels and the sound-speed perturbations present in the simulation indicates major disagreements with the measured travel-time shifts. These findings do not substantially change with the application of a correction for the reduction of wave amplitudes in the simulated and real sunspots. Overall, our findings demonstrate the need for new methods for inferring the subsurface structure of sunspots through helioseismic inversions.
Trend prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
Li Aiguo; Zhao Cai; Li Zhanhuai
2007-01-01
To predict the trend of chaotic time series in time series analysis and time series data mining fields, a novel predicting algorithm of chaotic time series trend is presented, and an on-line segmenting algorithm is proposed to convert a time series into a binary string according to ascending or descending trend of each subsequence. The on-line segmenting algorithm is independent of the prior knowledge about time series. The naive Bayesian algorithm is then employed to predict the trend of chaotic time series according to the binary string. The experimental results of three chaotic time series demonstrate that the proposed method predicts the ascending or descending trend of chaotic time series with few error.
In-depth survey of sunspot and active region catalogs
Lefèvre, Laure; Clette, Frédéric; Baranyi, Tunde
2011-08-01
When consulting detailed photospheric catalogs for solar activity studies spanning long time intervals, solar physicists face multiple limitations in the existing catalogs: finite or fragmented time coverage, limited time overlap between catalogs and even more importantly, a mismatch in contents and conventions. In view of a study of new sunspot-based activity indices, we have conducted a comprehensive survey of existing catalogs. In a first approach, we illustrate how the information from parallel catalogs can be merged to form a much more comprehensive record of sunspot groups. For this, we use the unique Debrecen Photoheliographic Data (DPD), which is already a composite of several ground observatories and SOHO data, and the USAF/Mount Wilson catalog from the Solar Optical Observing Network (SOON). We also describe our semi-interactive cross-identification method, which was needed to match the non-overlapping solar active region nomenclature, the most critical and subtle step when working with multiple catalogs. This effort, focused here first on the last two solar cycles, should lead to a better central database collecting all available sunspot group parameters to address future solar cycle studies beyond the traditional sunspot index time series Ri.
Predicting Physical Time Series Using Dynamic Ridge Polynomial Neural Networks
Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir
2014-01-01
Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques. PMID:25157950
Predicting physical time series using dynamic ridge polynomial neural networks.
Directory of Open Access Journals (Sweden)
Dhiya Al-Jumeily
Full Text Available Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques.
A Course in Time Series Analysis
Peña, Daniel; Tsay, Ruey S
2011-01-01
New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, a
Description of complex time series by multipoles
DEFF Research Database (Denmark)
Lewkowicz, M.; Levitan, J.; Puzanov, N.
2002-01-01
We present a new method to describe time series with a highly complex time evolution. The time series is projected onto a two-dimensional phase-space plot which is quantified in terms of a multipole expansion where every data point is assigned a unit mass. The multipoles provide an efficient...... characterization of the original time series....
Directory of Open Access Journals (Sweden)
D. M. Willis
2006-10-01
Full Text Available The validity of a technique developed by the authors to identify historical occurrences of intense geomagnetic storms, which is based on finding approximately coincident observations of sunspots and aurorae recorded in East Asian histories, is corroborated using more modern sunspot and auroral observations. Scientific observations of aurorae in Japan during the interval 1957–2004 are used to identify geomagnetic storms that are sufficiently intense to produce auroral displays at low geomagnetic latitudes. By examining white-light images of the Sun obtained by the Royal Greenwich Observatory, the Big Bear Solar Observatory, the Debrecen Heliophysical Observatory and the Solar and Heliospheric Observatory spacecraft, it is found that a sunspot large enough to be seen with the unaided eye by an "experienced" observer was located reasonably close to the central solar meridian immediately before all but one of the 30 distinct Japanese auroral events, which represents a 97% success rate. Even an "average" observer would probably have been able to see a sunspot with the unaided eye before 24 of these 30 events, which represents an 80% success rate. This corroboration of the validity of the technique used to identify historical occurences of intense geomagnetic storms is important because early unaided-eye observations of sunspots and aurorae provide the only possible means of identifying individual historical geomagnetic storms during the greater part of the past two millennia.
Yurchyshyn, Vasyl; Kilcik, Ali
2014-01-01
We analyse sunspot oscillations using Interface Region Imaging Spectrograph (IRIS) slit-jaw and spectral data and narrow-band chromospheric images from the New Solar Telescope (NST) for the main sunspot in NOAA AR 11836. We report that the difference between the shock arrival times as measured the Mg II k 2796.35\\AA\\ and Si IV 1393.76\\AA\\ line formation levels changes during the observed period and peak-to-peak delays may range from 40~s to zero. The intensity of chromospheric shocks also displays a long term (about 20~min) variations. NST's high spatial resolution \\ha\\ data allowed us to conclude that in this sunspot umbral flashes (UFs) appeared in the form of narrow bright lanes stretched along the light bridges and around clusters of umbral bright points. Time series also suggested that UFs preferred to appear on the sunspot-center side of light bridges, which may indicate the existence of a compact sub-photospheric driver of sunspot oscillations. The sunspot's umbra as seen in the IRIS chromospheric and ...
Recurrence plots of sunspots, solar flux and irradiance
Sparavigna, Amelia
2008-01-01
The paper shows the recurrence and cross recurrence plots of three time series, concerning data of the solar activity. The data are the sunspot number and the values of solar radio flux at 10.7 cm and of solar total irradiance, which are known as highly correlated. To compare the series, the radio flux and irradiance values are monthly averaged. Recurrence plots display the oscillating behaviour with remarkable features. Moreover, cross recurrence plots help in identifying time lags between the sunspot number maximum and the maximum of radio or irradiance signals, in circumstances where the data values are highly dispersed. Image processing is useful too, in enhancing the monitoring. An interesting behaviour is displayed by cross recurrence plots of irradiance, which are not symmetric with respect to the line of identity.
Effective Feature Preprocessing for Time Series Forecasting
DEFF Research Database (Denmark)
Zhao, Junhua; Dong, Zhaoyang; Xu, Zhao
2006-01-01
Time series forecasting is an important area in data mining research. Feature preprocessing techniques have significant influence on forecasting accuracy, therefore are essential in a forecasting model. Although several feature preprocessing techniques have been applied in time series forecasting...... performance in time series forecasting. It is demonstrated in our experiment that, effective feature preprocessing can significantly enhance forecasting accuracy. This research can be a useful guidance for researchers on effectively selecting feature preprocessing techniques and integrating them with time...... series forecasting models....
Sunspot Rotation as a Driver of Major Solar Eruptions in the NOAA Active Region 12158
Vemareddy, P.; Cheng, X.; Ravindra, B.
2016-09-01
We studied the development conditions of sigmoid structure under the influence of the magnetic non-potential characteristics of a rotating sunspot in the active region (AR) 12158. Vector magnetic field measurements from the Helioseismic Magnetic Imager and coronal EUV observations from the Atmospheric Imaging Assembly reveal that the erupting inverse-S sigmoid had roots at the location of the rotating sunspot. The sunspot rotates at a rate of 0°-5° h-1 with increasing trend in the first half followed by a decrease. The time evolution of many non-potential parameters had a good correspondence with the sunspot rotation. The evolution of the AR magnetic structure is approximated by a time series of force-free equilibria. The non-linear force-free field magnetic structure around the sunspot manifests the observed sigmoid structure. Field lines from the sunspot periphery constitute the body of the sigmoid and those from the interior overlie the sigmoid, similar to a flux rope structure. While the sunspot was rotating, two major coronal mass ejection eruptions occurred in the AR. During the first (second) event, the coronal current concentrations were enhanced (degraded), consistent with the photospheric net vertical current; however, magnetic energy was released during both cases. The analysis results suggest that the magnetic connections of the sigmoid are driven by the slow motion of sunspot rotation, which transforms to a highly twisted flux rope structure in a dynamical scenario. Exceeding the critical twist in the flux rope probably leads to the loss of equilibrium, thus triggering the onset of the two eruptions.
Regenerating time series from ordinal networks
McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael
2017-03-01
Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.
Regenerating time series from ordinal networks.
McCullough, Michael; Sakellariou, Konstantinos; Stemler, Thomas; Small, Michael
2017-03-01
Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.
Time Series Analysis and Forecasting by Example
Bisgaard, Soren
2011-01-01
An intuition-based approach enables you to master time series analysis with ease Time Series Analysis and Forecasting by Example provides the fundamental techniques in time series analysis using various examples. By introducing necessary theory through examples that showcase the discussed topics, the authors successfully help readers develop an intuitive understanding of seemingly complicated time series models and their implications. The book presents methodologies for time series analysis in a simplified, example-based approach. Using graphics, the authors discuss each presented example in
Subsurface magnetic field and flow structure of simulated sunspots
Rempel, Matthias
2011-01-01
We present a series of numerical sunspot models addressing the subsurface field and flow structure in up to 16 Mm deep domains covering up to 2 days of temporal evolution. Changes in the photospheric appearance of the sunspots are driven by subsurface flows in several Mm depth. Most of magnetic field is pushed into a downflow vertex of the subsurface convection pattern, while some fraction of the flux separates from the main trunk of the spot. Flux separation in deeper layers is accompanied in the photosphere with light bridge formation in the early stages and formation of pores separating from the spot at later stages. Over a time scale of less than a day we see the development of a large scale flow pattern surrounding the sunspots, which is dominated by a radial outflow reaching about 50% of the convective rms velocity in amplitude. Several components of the large scale flow are found to be independent from the presence of a penumbra and the associated Evershed flow. While the simulated sunspots lead to blo...
Duality between Time Series and Networks
Campanharo, Andriana S. L. O.; Sirer, M. Irmak; Malmgren, R. Dean; Ramos, Fernando M.; Amaral, Luís A. Nunes.
2011-01-01
Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways. PMID:21858093
A Review of Subsequence Time Series Clustering
Teh, Ying Wah
2014-01-01
Clustering of subsequence time series remains an open issue in time series clustering. Subsequence time series clustering is used in different fields, such as e-commerce, outlier detection, speech recognition, biological systems, DNA recognition, and text mining. One of the useful fields in the domain of subsequence time series clustering is pattern recognition. To improve this field, a sequence of time series data is used. This paper reviews some definitions and backgrounds related to subsequence time series clustering. The categorization of the literature reviews is divided into three groups: preproof, interproof, and postproof period. Moreover, various state-of-the-art approaches in performing subsequence time series clustering are discussed under each of the following categories. The strengths and weaknesses of the employed methods are evaluated as potential issues for future studies. PMID:25140332
Neural modeling for time series: A statistical stepwise method for weight elimination.
Cottrell, M; Girard, B; Girard, Y; Mangeas, M; Muller, C
1995-01-01
Many authors use feedforward neural networks for modeling and forecasting time series. Most of these applications are mainly experimental, and it is often difficult to extract a general methodology from the published studies. In particular, the choice of architecture is a tricky problem. We try to combine the statistical techniques of linear and nonlinear time series with the connectionist approach. The asymptotical properties of the estimators lead us to propose a systematic methodology to determine which weights are nonsignificant and to eliminate them to simplify the architecture. This method (SSM or statistical stepwise method) is compared to other pruning techniques and is applied to some artificial series, to the famous Sunspots benchmark, and to daily electrical consumption data.
Re-evaluation of Predictive Models in Light of New Data: Sunspot Number Version 2.0
Gkana, A.; Zachilas, L.
2016-10-01
The original version of the Zürich sunspot number (Sunspot Number Version 1.0) has been revised by an entirely new series (Sunspot Number Version 2.0). We re-evaluate the performance of our previously proposed models for predicting solar activity in the light of the revised data. We perform new monthly and yearly predictions using the Sunspot Number Version 2.0 as input data and compare them with our original predictions (using the Sunspot Number Version 1.0 series as input data). We show that our previously proposed models are still able to produce quite accurate solar-activity predictions despite the full revision of the Zürich Sunspot Number, indicating that there is no significant degradation in their performance. Extending our new monthly predictions (July 2013 - August 2015) by 50 time-steps (months) ahead in time (from September 2015 to October 2019), we provide evidence that we are heading into a period of dramatically low solar activity. Finally, our new future long-term predictions endorse our previous claim that a prolonged solar activity minimum is expected to occur, lasting up to the year ≈ 2100.
Uncertainties in the Sunspot Numbers: Estimation and Implications
de Wit, Thierry Dudok; Clette, Frédéric
2016-01-01
Sunspot number series are subject to various uncertainties, which are still poorly known. The need for their better understanding was recently highlighted by the major makeover of the international Sunspot Number [Clette et al., Space Science Reviews, 2014]. We present the first thorough estimation of these uncertainties, which behave as Poisson-like random variables with a multiplicative coefficient that is time- and observatory-dependent. We provide a simple expression for these uncertainties, and reveal how their evolution in time coincides with changes in the observations, and processing of the data. Knowing their value is essential for properly building composites out of multiple observations, and for preserving the stability of the composites in time.
Data mining in time series databases
Kandel, Abraham; Bunke, Horst
2004-01-01
Adding the time dimension to real-world databases produces Time SeriesDatabases (TSDB) and introduces new aspects and difficulties to datamining and knowledge discovery. This book covers the state-of-the-artmethodology for mining time series databases. The novel data miningmethods presented in the book include techniques for efficientsegmentation, indexing, and classification of noisy and dynamic timeseries. A graph-based method for anomaly detection in time series isdescribed and the book also studies the implications of a novel andpotentially useful representation of time series as strings. Theproblem of detecting changes in data mining models that are inducedfrom temporal databases is additionally discussed.
Outliers Mining in Time Series Data Sets
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, we present a cluster-based algorithm for time series outlier mining.We use discrete Fourier transformation (DFT) to transform time series from time domain to frequency domain. Time series thus can be mapped as the points in k-dimensional space.For these points, a cluster-based algorithm is developed to mine the outliers from these points.The algorithm first partitions the input points into disjoint clusters and then prunes the clusters,through judgment that can not contain outliers.Our algorithm has been run in the electrical load time series of one steel enterprise and proved to be effective.
International Work-Conference on Time Series
Pomares, Héctor
2016-01-01
This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.
Coupling between time series: a network view
Mehraban, Saeed; Zamani, Maryam; Jafari, Gholamreza
2013-01-01
Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mapped to a network, "the cross-visibility graph", to demonstrate the correlation between them. We applied the algorithm to several correlated and uncorrelated time series, generated by the linear stationary ARFIMA process. The results demonstrate that the cross-visibility graph associated with correlated time series with power-law auto-correlation is scale-free. If the time series are uncorrelated, the degree distribution of their cross-visibility network deviates from power-law. For more clarifying the process, we applied the algorithm to real-world data from the financial trades of two companies, and observed significant small-scale coupling in their dynamics.
Planetary model of sunspot emergence: A spectral and autocorrelation analysis
Edmonds, Ian
2016-01-01
This paper is concerned with intermediate range periodicity in the sunspot area spectrum. An empirical model of sunspot area emergence based on Mercury planet conjunctions was developed and the spectra of the model variation and the sunspot area variation compared. By including solar cycle amplitude modulation and the effect of solar magnetic field reversal the model was able to predict fine detail in the sunspot area spectrum. As Mercury planet conjunctions occur predictably it was possible to compare the time variation of band limited components of sunspot area with the corresponding component variations in the model. When the model component variation was stable corresponding components of sunspot area lagged the model variation by a few tens of days. When a 180 degree phase change occurred in the model variation the corresponding component of sunspot area followed the change over an interval of a few hundred days, first by decreasing to zero and then emerging in phase with the model variation. Where perio...
Forecasting Enrollments with Fuzzy Time Series.
Song, Qiang; Chissom, Brad S.
The concept of fuzzy time series is introduced and used to forecast the enrollment of a university. Fuzzy time series, an aspect of fuzzy set theory, forecasts enrollment using a first-order time-invariant model. To evaluate the model, the conventional linear regression technique is applied and the predicted values obtained are compared to the…
The Amplitude Density Function and High-Resolution Frequency Analysis of Time Series.
1983-09-06
Math. Astr. Fsik., 28, 1-7. CURRIE, R. G. (1980), "Detection of the 11-year Sunspot Cycle in Earth Rotation" . Geophys. J. R. Astr. Soc., 61, 131-140...enhanced precision and number of torsional eigenperiods detected from data recorded at Trieste following -2- the 1960 Chilean earthquake . The maxzin...the use of a physically motivated data transfotmation of the sunspot series which drmatically Isproves the performce of the model described In Section
Directory of Open Access Journals (Sweden)
D. M. Willis
2009-01-01
Full Text Available A further study is made of the validity of a technique developed by the authors to identify historical occurrences of intense geomagnetic storms, which is based on finding approximately coincident observations of sunspots and aurorae recorded in East Asian histories. Previously, the validity of this technique was corroborated using scientific observations of aurorae in Japan during the interval 1957–2004 and contemporaneous white-light images of the Sun obtained by the Royal Greenwich Observatory, the Big Bear Solar Observatory, the Debrecen Heliophysical Observatory, and the Solar and Heliospheric Observatory spacecraft. The present investigation utilises a list of major geomagnetic storms in the interval 1868–2008, which is based on the magnitude of the AA* magnetic index, and reconstructed solar images based on the sunspot observations acquired by the Royal Greenwich Observatory during the shorter interval 1874–1976. It is found that a sunspot large enough to be seen with the unaided eye by an "experienced" observer was located reasonably close to the central solar meridian for almost 90% of these major geomagnetic storms. Even an "average" observer would easily achieve a corresponding success rate of 70% and this success rate increases to about 80% if a minority of ambiguous situations are interpreted favourably. The use of information on major geomagnetic storms, rather than modern auroral observations from Japan, provides a less direct corroboration of the technique for identifying historical occurrences of intense geomagnetic storms, if only because major geomagnetic storms do not necessarily produce auroral displays over East Asia. Nevertheless, the present study provides further corroboration of the validity of the original technique for identifying intense geomagnetic storms. This additional corroboration of the original technique is important because early unaided-eye observations of sunspots and aurorae provide the only
Hurst Exponent Analysis of Financial Time Series
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Statistical properties of stock market time series and the implication of their Hurst exponents are discussed. Hurst exponents of DJ1A (Dow Jones Industrial Average) components are tested using re-scaled range analysis. In addition to the original stock return series, the linear prediction errors of the daily returns are also tested. Numerical results show that the Hurst exponent analysis can provide some information about the statistical properties of the financial time series.
Transfer entropy between multivariate time series
Mao, Xuegeng; Shang, Pengjian
2017-06-01
It is a crucial topic to identify the direction and strength of the interdependence between time series in multivariate systems. In this paper, we propose the method of transfer entropy based on the theory of time-delay reconstruction of a phase space, which is a model-free approach to detect causalities in multivariate time series. This method overcomes the limitation that original transfer entropy only can capture which system drives the transition probabilities of another in scalar time series. Using artificial time series, we show that the driving character is obviously reflected with the increase of the coupling strength between two signals and confirm the effectiveness of the method with noise added. Furthermore, we utilize it to real-world data, namely financial time series, in order to characterize the information flow among different stocks.
Statistical criteria for characterizing irradiance time series.
Energy Technology Data Exchange (ETDEWEB)
Stein, Joshua S.; Ellis, Abraham; Hansen, Clifford W.
2010-10-01
We propose and examine several statistical criteria for characterizing time series of solar irradiance. Time series of irradiance are used in analyses that seek to quantify the performance of photovoltaic (PV) power systems over time. Time series of irradiance are either measured or are simulated using models. Simulations of irradiance are often calibrated to or generated from statistics for observed irradiance and simulations are validated by comparing the simulation output to the observed irradiance. Criteria used in this comparison should derive from the context of the analyses in which the simulated irradiance is to be used. We examine three statistics that characterize time series and their use as criteria for comparing time series. We demonstrate these statistics using observed irradiance data recorded in August 2007 in Las Vegas, Nevada, and in June 2009 in Albuquerque, New Mexico.
Wavelet-based multifractal analysis on a time series of solar activity and PDO climate index
Maruyama, Fumio; Kai, Kenji; Morimoto, Hiroshi
2017-09-01
There is increasing interest in finding the relation between solar activity and climate change. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigates the relations among solar activity, geomagnetic activity, and climatic regime shift by performing a multifractal analysis. To investigate the change in multifractality, we apply a wavelet transform to time series. The change in fractality of the sunspot number (SSN) correlates closely with that of the solar polar field strength. For the SSN and solar polar field strength, a weak multifractality or monofractality is present at the maximum SSN, minimum SSN, and maximum solar polar field strength. A strong multifractality is present two years before the maximum SSN. The climatic regime shift occurs when the SSN increases and the disturbance of the geomagnetic activity is large. At the climatic regime shift, the changes in the fractality of the Pacific Decadal Oscillation (PDO) index and changes in that of the solar activity indices corresponded with each other. From the fractals point of view, we clarify the relations among solar activity, geomagnetic activity, and climatic regime shift. The formation of the magnetic field of the sunspots is correlated with the solar polar field strength. The solar activity seems to influence the climatic regime shift. These findings will contribute to investigating the relation between solar activity and climate change.
Reconstruction of time-delay systems from chaotic time series.
Bezruchko, B P; Karavaev, A S; Ponomarenko, V I; Prokhorov, M D
2001-11-01
We propose a method that allows one to estimate the parameters of model scalar time-delay differential equations from time series. The method is based on a statistical analysis of time intervals between extrema in the time series. We verify our method by using it for the reconstruction of time-delay differential equations from their chaotic solutions and for modeling experimental systems with delay-induced dynamics from their chaotic time series.
Lag space estimation in time series modelling
DEFF Research Database (Denmark)
Goutte, Cyril
1997-01-01
The purpose of this article is to investigate some techniques for finding the relevant lag-space, i.e. input information, for time series modelling. This is an important aspect of time series modelling, as it conditions the design of the model through the regressor vector a.k.a. the input layer...
The foundations of modern time series analysis
Mills, Terence C
2011-01-01
This book develops the analysis of Time Series from its formal beginnings in the 1890s through to the publication of Box and Jenkins' watershed publication in 1970, showing how these methods laid the foundations for the modern techniques of Time Series analysis that are in use today.
Self-organising mixture autoregressive model for non-stationary time series modelling.
Ni, He; Yin, Hujun
2008-12-01
Modelling non-stationary time series has been a difficult task for both parametric and nonparametric methods. One promising solution is to combine the flexibility of nonparametric models with the simplicity of parametric models. In this paper, the self-organising mixture autoregressive (SOMAR) network is adopted as a such mixture model. It breaks time series into underlying segments and at the same time fits local linear regressive models to the clusters of segments. In such a way, a global non-stationary time series is represented by a dynamic set of local linear regressive models. Neural gas is used for a more flexible structure of the mixture model. Furthermore, a new similarity measure has been introduced in the self-organising network to better quantify the similarity of time series segments. The network can be used naturally in modelling and forecasting non-stationary time series. Experiments on artificial, benchmark time series (e.g. Mackey-Glass) and real-world data (e.g. numbers of sunspots and Forex rates) are presented and the results show that the proposed SOMAR network is effective and superior to other similar approaches.
Leberl, F.; Fuchs, H.; Ford, J. P.
1981-01-01
A set of ten side-looking radar images of a mining area in Arizona that were aquired over a period of 14 yr are studied to demonstrate the photogrammetric differential-rectification technique applied to radar images and to examine changes that occurred in the area over time. Five of the images are rectified by using ground control points and a digital height model taken from a map. Residual coordinate errors in ground control are reduced from several hundred meters in all cases to + or - 19 to 70 m. The contents of the radar images are compared with a Landsat image and with aerial photographs. Effects of radar system parameters on radar images are briefly reviewed.
Biclustering of time series microarray data.
Meng, Jia; Huang, Yufei
2012-01-01
Clustering is a popular data exploration technique widely used in microarray data analysis. In this chapter, we review ideas and algorithms of bicluster and its applications in time series microarray analysis. We introduce first the concept and importance of biclustering and its different variations. We then focus our discussion on the popular iterative signature algorithm (ISA) for searching biclusters in microarray dataset. Next, we discuss in detail the enrichment constraint time-dependent ISA (ECTDISA) for identifying biologically meaningful temporal transcription modules from time series microarray dataset. In the end, we provide an example of ECTDISA application to time series microarray data of Kaposi's Sarcoma-associated Herpesvirus (KSHV) infection.
Support vector echo-state machine for chaotic time-series prediction.
Shi, Zhiwei; Han, Min
2007-03-01
A novel chaotic time-series prediction method based on support vector machines (SVMs) and echo-state mechanisms is proposed. The basic idea is replacing "kernel trick" with "reservoir trick" in dealing with nonlinearity, that is, performing linear support vector regression (SVR) in the high-dimension "reservoir" state space, and the solution benefits from the advantages from structural risk minimization principle, and we call it support vector echo-state machines (SVESMs). SVESMs belong to a special kind of recurrent neural networks (RNNs) with convex objective function, and their solution is global, optimal, and unique. SVESMs are especially efficient in dealing with real life nonlinear time series, and its generalization ability and robustness are obtained by regularization operator and robust loss function. The method is tested on the benchmark prediction problem of Mackey-Glass time series and applied to some real life time series such as monthly sunspots time series and runoff time series of the Yellow River, and the prediction results are promising.
The Impact of the Revised Sunspot Record on Solar Irradiance Reconstructions
Kopp, G.; Krivova, N.; Wu, C. J.; Lean, J.
2016-11-01
Reliable historical records of the total solar irradiance (TSI) are needed to assess the extent to which long-term variations in the Sun's radiant energy that is incident upon Earth may exacerbate (or mitigate) the more dominant warming in recent centuries that is due to increasing concentrations of greenhouse gases. We investigate the effects that the new Sunspot Index and Long-term Solar Observations (SILSO) sunspot-number time series may have on model reconstructions of the TSI. In contemporary TSI records, variations on timescales longer than about a day are dominated by the opposing effects of sunspot darkening and facular brightening. These two surface magnetic features, retrieved either from direct observations or from solar-activity proxies, are combined in TSI models to reproduce the current TSI observational record. Indices that manifest solar-surface magnetic activity, in particular the sunspot-number record, then enable reconstructing historical TSI. Revisions of the sunspot-number record therefore affect the magnitude and temporal structure of TSI variability on centennial timescales according to the model reconstruction methods that are employed. We estimate the effects of the new SILSO record on two widely used TSI reconstructions, namely the NRLTSI2 and the SATIRE models. We find that the SILSO record has little effect on either model after 1885, but leads to solar-cycle fluctuations with greater amplitude in the TSI reconstructions prior. This suggests that many eighteenth- and nineteenth-century cycles could be similar in amplitude to those of the current Modern Maximum. TSI records based on the revised sunspot data do not suggest a significant change in Maunder Minimum TSI values, and from comparing this era to the present, we find only very small potential differences in the estimated solar contributions to the climate with this new sunspot record.
Developing consistent time series landsat data products
The Landsat series satellite has provided earth observation data record continuously since early 1970s. There are increasing demands on having a consistent time series of Landsat data products. In this presentation, I will summarize the work supported by the USGS Landsat Science Team project from 20...
Modeling Time Series Data for Supervised Learning
Baydogan, Mustafa Gokce
2012-01-01
Temporal data are increasingly prevalent and important in analytics. Time series (TS) data are chronological sequences of observations and an important class of temporal data. Fields such as medicine, finance, learning science and multimedia naturally generate TS data. Each series provide a high-dimensional data vector that challenges the learning…
DATA MINING IN CANADIAN LYNX TIME SERIES
Directory of Open Access Journals (Sweden)
R.Karnaboopathy
2012-01-01
Full Text Available This paper sums up the applications of Statistical model such as ARIMA family timeseries models in Canadian lynx data time series analysis and introduces the method of datamining combined with Statistical knowledge to analysis Canadian lynx data series.
Time Series Analysis Forecasting and Control
Box, George E P; Reinsel, Gregory C
2011-01-01
A modernized new edition of one of the most trusted books on time series analysis. Since publication of the first edition in 1970, Time Series Analysis has served as one of the most influential and prominent works on the subject. This new edition maintains its balanced presentation of the tools for modeling and analyzing time series and also introduces the latest developments that have occurred n the field over the past decade through applications from areas such as business, finance, and engineering. The Fourth Edition provides a clearly written exploration of the key methods for building, cl
A Simple Fuzzy Time Series Forecasting Model
DEFF Research Database (Denmark)
Ortiz-Arroyo, Daniel
2016-01-01
In this paper we describe a new ﬁrst order fuzzy time series forecasting model. We show that our automatic fuzzy partitioning method provides an accurate approximation to the time series that when combined with rule forecasting and an OWA operator improves forecasting accuracy. Our model does...... not attempt to provide the best results in comparison with other forecasting methods but to show how to improve ﬁrst order models using simple techniques. However, we show that our ﬁrst order model is still capable of outperforming some more complex higher order fuzzy time series models....
Time series modeling, computation, and inference
Prado, Raquel
2010-01-01
The authors systematically develop a state-of-the-art analysis and modeling of time series. … this book is well organized and well written. The authors present various statistical models for engineers to solve problems in time series analysis. Readers no doubt will learn state-of-the-art techniques from this book.-Hsun-Hsien Chang, Computing Reviews, March 2012My favorite chapters were on dynamic linear models and vector AR and vector ARMA models.-William Seaver, Technometrics, August 2011… a very modern entry to the field of time-series modelling, with a rich reference list of the current lit
Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction
Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.
2012-01-01
In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS docume
Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction
Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.
2012-01-01
In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS docume
Forecasting Daily Time Series using Periodic Unobserved Components Time Series Models
Koopman, Siem Jan; Ooms, Marius
2004-01-01
We explore a periodic analysis in the context of unobserved components time series models that decompose time series into components of interest such as trend and seasonal. Periodic time series models allow dynamic characteristics to depend on the period of the year, month, week or day. In the stand
Forecasting Daily Time Series using Periodic Unobserved Components Time Series Models
Koopman, Siem Jan; Ooms, Marius
2004-01-01
We explore a periodic analysis in the context of unobserved components time series models that decompose time series into components of interest such as trend and seasonal. Periodic time series models allow dynamic characteristics to depend on the period of the year, month, week or day. In the
Evaluation of Harmonic Analysis of Time Series (HANTS): impact of gaps on time series reconstruction
Zhou, J.Y.; Jia, L.; Hu, G.; Menenti, M.
2012-01-01
In recent decades, researchers have developed methods and models to reconstruct time series of irregularly spaced observations from satellite remote sensing, among which the widely used Harmonic Analysis of Time Series (HANTS) method. Many studies based on time series reconstructed with HANTS
Visibility Graph Based Time Series Analysis.
Stephen, Mutua; Gu, Changgui; Yang, Huijie
2015-01-01
Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.
Visibility Graph Based Time Series Analysis
Stephen, Mutua; Gu, Changgui; Yang, Huijie
2015-01-01
Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it’s microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks. PMID:26571115
Measuring nonlinear behavior in time series data
Wai, Phoong Seuk; Ismail, Mohd Tahir
2014-12-01
Stationary Test is an important test in detect the time series behavior since financial and economic data series always have missing data, structural change as well as jumps or breaks in the data set. Moreover, stationary test is able to transform the nonlinear time series variable to become stationary by taking difference-stationary process or trend-stationary process. Two different types of hypothesis testing of stationary tests that are Augmented Dickey-Fuller (ADF) test and Kwiatkowski-Philips-Schmidt-Shin (KPSS) test are examine in this paper to describe the properties of the time series variables in financial model. Besides, Least Square method is used in Augmented Dickey-Fuller test to detect the changes of the series and Lagrange multiplier is used in Kwiatkowski-Philips-Schmidt-Shin test to examine the properties of oil price, gold price and Malaysia stock market. Moreover, Quandt-Andrews, Bai-Perron and Chow tests are also use to detect the existence of break in the data series. The monthly index data are ranging from December 1989 until May 2012. Result is shown that these three series exhibit nonlinear properties but are able to transform to stationary series after taking first difference process.
Applied time series analysis and innovative computing
Ao, Sio-Iong
2010-01-01
This text is a systematic, state-of-the-art introduction to the use of innovative computing paradigms as an investigative tool for applications in time series analysis. It includes frontier case studies based on recent research.
Spectra: Time series power spectrum calculator
Gallardo, Tabaré
2017-01-01
Spectra calculates the power spectrum of a time series equally spaced or not based on the Spectral Correlation Coefficient (Ferraz-Mello 1981, Astron. Journal 86 (4), 619). It is very efficient for detection of low frequencies.
Improving Intercomparability of Marine Biogeochemical Time Series
Benway, Heather M.; Telszewski, Maciej; Lorenzoni, Laura
2013-04-01
Shipboard biogeochemical time series represent one of the most valuable tools scientists have to quantify marine elemental fluxes and associated biogeochemical processes and to understand their links to changing climate. They provide the long, temporally resolved data sets needed to characterize ocean climate, biogeochemistry, and ecosystem variability and change. However, to monitor and differentiate natural cycles and human-driven changes in the global oceans, time series methodologies must be transparent and intercomparable when possible. To review current shipboard biogeochemical time series sampling and analytical methods, the International Ocean Carbon Coordination Project (IOCCP; http://www.ioccp.org/) and the Ocean Carbon and Biogeochemistry Program (http://www.us-ocb.org/) convened an international ocean time series workshop at the Bermuda Institute for Ocean Sciences.
FATS: Feature Analysis for Time Series
Nun, Isadora; Sim, Brandon; Zhu, Ming; Dave, Rahul; Castro, Nicolas; Pichara, Karim
2015-01-01
In this paper, we present the FATS (Feature Analysis for Time Series) library. FATS is a Python library which facilitates and standardizes feature extraction for time series data. In particular, we focus on one application: feature extraction for astronomical light curve data, although the library is generalizable for other uses. We detail the methods and features implemented for light curve analysis, and present examples for its usage.
Combination prediction method of chaotic time series
Institute of Scientific and Technical Information of China (English)
ZHAO DongHua; RUAN Jiong; CAI ZhiJie
2007-01-01
In the present paper, we propose an approach of combination prediction of chaotic time series. The method is based on the adding-weight one-rank local-region method of chaotic time series. The method allows us to define an interval containing a future value with a given probability, which is obtained by studying the prediction error distribution. Its effectiveness is shown with data generated by Logistic map.
Pseudotime estimation: deconfounding single cell time series
John E Reid; Wernisch, Lorenz
2016-01-01
Motivation: Repeated cross-sectional time series single cell data confound several sources of variation, with contributions from measurement noise, stochastic cell-to-cell variation and cell progression at different rates. Time series from single cell assays are particularly susceptible to confounding as the measurements are not averaged over populations of cells. When several genes are assayed in parallel these effects can be estimated and corrected for under certain smoothness assumptions o...
Introduction to time series analysis and forecasting
Montgomery, Douglas C; Kulahci, Murat
2008-01-01
An accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data. Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.
Testing for nonlinearity in time series: The method of surrogate data
Energy Technology Data Exchange (ETDEWEB)
Theiler, J.; Galdrikian, B.; Longtin, A. (Los Alamos National Lab., NM (United States)); Eubank, S.; Farmer, J.D. (Los Alamos National Lab., NM (United States) Santa Fe Inst., NM (United States))
1991-01-01
We describe a statistical approach for identifying nonlinearity in time series; in particular, we want to avoid claims of chaos when simpler models (such as linearly correlated noise) can explain the data. The method requires a careful statement of the null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. We present algorithms for generating surrogate data under various null hypotheses, and we show the results of numerical experiments on artificial data using correlation dimension, Lyapunov exponent, and forecasting error as discriminating statistics. Finally, we consider a number of experimental time series -- including sunspots, electroencephalogram (EEG) signals, and fluid convection -- and evaluate the statistical significance of the evidence for nonlinear structure in each case. 56 refs., 8 figs.
Time Series Forecasting with Missing Values
Directory of Open Access Journals (Sweden)
Shin-Fu Wu
2015-11-01
Full Text Available Time series prediction has become more popular in various kinds of applications such as weather prediction, control engineering, financial analysis, industrial monitoring, etc. To deal with real-world problems, we are often faced with missing values in the data due to sensor malfunctions or human errors. Traditionally, the missing values are simply omitted or replaced by means of imputation methods. However, omitting those missing values may cause temporal discontinuity. Imputation methods, on the other hand, may alter the original time series. In this study, we propose a novel forecasting method based on least squares support vector machine (LSSVM. We employ the input patterns with the temporal information which is defined as local time index (LTI. Time series data as well as local time indexes are fed to LSSVM for doing forecasting without imputation. We compare the forecasting performance of our method with other imputation methods. Experimental results show that the proposed method is promising and is worth further investigations.
Time averaging, ageing and delay analysis of financial time series
Cherstvy, Andrey G.; Vinod, Deepak; Aghion, Erez; Chechkin, Aleksei V.; Metzler, Ralf
2017-06-01
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
Feature Matching in Time Series Modelling
Xia, Yingcun
2011-01-01
Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In the absence of a true model, we prefer an alternative approach to conventional model fitting that typically involves one-step-ahead prediction errors. Our primary aim is to match the joint probability distribution of the observable time series, including long-term features of the dynamics that underpin the data, such as cycles, long memory and others, rather than short-term prediction. For want of a better name, we call this specific aim {\\it feature matching}. The challenges of model mis-specification, measurement errors and the scarcity of data are forever present in real time series modelling. In this paper, by synthesizing earlier attempts into an extended-likelihood, we develop a systematic approach to empirical time series analysis to address these challenges and to aim at achieving...
Highly comparative time-series analysis: the empirical structure of time series and their methods.
Fulcher, Ben D; Little, Max A; Jones, Nick S
2013-06-06
The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording and analysing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods has never been performed. Addressing this, annotated collections of over 35 000 real-world and model-generated time series, and over 9000 time-series analysis algorithms are analysed in this work. We introduce reduced representations of both time series, in terms of their properties measured by diverse scientific methods, and of time-series analysis methods, in terms of their behaviour on empirical time series, and use them to organize these interdisciplinary resources. This new approach to comparing across diverse scientific data and methods allows us to organize time-series datasets automatically according to their properties, retrieve alternatives to particular analysis methods developed in other scientific disciplines and automate the selection of useful methods for time-series classification and regression tasks. The broad scientific utility of these tools is demonstrated on datasets of electroencephalograms, self-affine time series, heartbeat intervals, speech signals and others, in each case contributing novel analysis techniques to the existing literature. Highly comparative techniques that compare across an interdisciplinary literature can thus be used to guide more focused research in time-series analysis for applications across the scientific disciplines.
Predicting road accidents: Structural time series approach
Junus, Noor Wahida Md; Ismail, Mohd Tahir
2014-07-01
In this paper, the model for occurrence of road accidents in Malaysia between the years of 1970 to 2010 was developed and throughout this model the number of road accidents have been predicted by using the structural time series approach. The models are developed by using stepwise method and the residual of each step has been analyzed. The accuracy of the model is analyzed by using the mean absolute percentage error (MAPE) and the best model is chosen based on the smallest Akaike information criterion (AIC) value. A structural time series approach found that local linear trend model is the best model to represent the road accidents. This model allows level and slope component to be varied over time. In addition, this approach also provides useful information on improving the conventional time series method.
Effective Feature Preprocessing for Time Series Forecasting
DEFF Research Database (Denmark)
Zhao, Junhua; Dong, Zhaoyang; Xu, Zhao
2006-01-01
Time series forecasting is an important area in data mining research. Feature preprocessing techniques have significant influence on forecasting accuracy, therefore are essential in a forecasting model. Although several feature preprocessing techniques have been applied in time series forecasting......, there is so far no systematic research to study and compare their performance. How to select effective techniques of feature preprocessing in a forecasting model remains a problem. In this paper, the authors conduct a comprehensive study of existing feature preprocessing techniques to evaluate their empirical...... performance in time series forecasting. It is demonstrated in our experiment that, effective feature preprocessing can significantly enhance forecasting accuracy. This research can be a useful guidance for researchers on effectively selecting feature preprocessing techniques and integrating them with time...
Introduction to time series analysis and forecasting
Montgomery, Douglas C; Kulahci, Murat
2015-01-01
Praise for the First Edition ""…[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics."" -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both
Weather variability, sunspots, and the blooms of cyanobacteria.
Hu, Wenbiao; Connell, Des; Mengersen, Kerrie; Tong, Shilu
2009-03-01
The roles of weather variability and sunspots in the occurrence of cyanobacteria blooms, were investigated using cyanobacteria cell data collected from the Fred Haigh Dam, Queensland, Australia. Time series generalized linear model and classification and regression tree (CART) model were used in the analysis. Data on notified cell numbers of cyanobacteria and weather variables over the periods 2001 and 2005 were provided by the Australian Department of Natural Resources and Water, and Australian Bureau of Meteorology, respectively. The results indicate that monthly minimum temperature (relative risk [RR]: 1.13, 95% confidence interval [CI]: 1.02-1.25) and rainfall (RR: 1.11; 95% CI: 1.03-1.20) had a positive association, but relative humidity (RR: 0.94; 95% CI: 0.91-0.98) and wind speed (RR: 0.90; 95% CI: 0.82-0.98) were negatively associated with the cyanobacterial numbers, after adjustment for seasonality and auto-correlation. The CART model showed that the cyanobacteria numbers were best described by an interaction between minimum temperature, relative humidity, and sunspot numbers. When minimum temperature exceeded 18 degrees C and relative humidity was under 66%, the number of cyanobacterial cells rose by 2.15-fold. We conclude that weather variability and sunspot activity may affect cyanobacteria blooms in dams.
Ridge Polynomial Neural Network with Error Feedback for Time Series Forecasting.
Waheeb, Waddah; Ghazali, Rozaida; Herawan, Tutut
2016-01-01
Time series forecasting has gained much attention due to its many practical applications. Higher-order neural network with recurrent feedback is a powerful technique that has been used successfully for time series forecasting. It maintains fast learning and the ability to learn the dynamics of the time series over time. Network output feedback is the most common recurrent feedback for many recurrent neural network models. However, not much attention has been paid to the use of network error feedback instead of network output feedback. In this study, we propose a novel model, called Ridge Polynomial Neural Network with Error Feedback (RPNN-EF) that incorporates higher order terms, recurrence and error feedback. To evaluate the performance of RPNN-EF, we used four univariate time series with different forecasting horizons, namely star brightness, monthly smoothed sunspot numbers, daily Euro/Dollar exchange rate, and Mackey-Glass time-delay differential equation. We compared the forecasting performance of RPNN-EF with the ordinary Ridge Polynomial Neural Network (RPNN) and the Dynamic Ridge Polynomial Neural Network (DRPNN). Simulation results showed an average 23.34% improvement in Root Mean Square Error (RMSE) with respect to RPNN and an average 10.74% improvement with respect to DRPNN. That means that using network errors during training helps enhance the overall forecasting performance for the network.
Building Chaotic Model From Incomplete Time Series
Siek, Michael; Solomatine, Dimitri
2010-05-01
This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual
Layered Ensemble Architecture for Time Series Forecasting.
Rahman, Md Mustafizur; Islam, Md Monirul; Murase, Kazuyuki; Yao, Xin
2016-01-01
Time series forecasting (TSF) has been widely used in many application areas such as science, engineering, and finance. The phenomena generating time series are usually unknown and information available for forecasting is only limited to the past values of the series. It is, therefore, necessary to use an appropriate number of past values, termed lag, for forecasting. This paper proposes a layered ensemble architecture (LEA) for TSF problems. Our LEA consists of two layers, each of which uses an ensemble of multilayer perceptron (MLP) networks. While the first ensemble layer tries to find an appropriate lag, the second ensemble layer employs the obtained lag for forecasting. Unlike most previous work on TSF, the proposed architecture considers both accuracy and diversity of the individual networks in constructing an ensemble. LEA trains different networks in the ensemble by using different training sets with an aim of maintaining diversity among the networks. However, it uses the appropriate lag and combines the best trained networks to construct the ensemble. This indicates LEAs emphasis on accuracy of the networks. The proposed architecture has been tested extensively on time series data of neural network (NN)3 and NN5 competitions. It has also been tested on several standard benchmark time series data. In terms of forecasting accuracy, our experimental results have revealed clearly that LEA is better than other ensemble and nonensemble methods.
Complex network analysis of time series
Gao, Zhong-Ke; Small, Michael; Kurths, Jürgen
2016-12-01
Revealing complicated behaviors from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. The past decade has witnessed a rapid development of complex network studies, which allow to characterize many types of systems in nature and technology that contain a large number of components interacting with each other in a complicated manner. Recently, the complex network theory has been incorporated into the analysis of time series and fruitful achievements have been obtained. Complex network analysis of time series opens up new venues to address interdisciplinary challenges in climate dynamics, multiphase flow, brain functions, ECG dynamics, economics and traffic systems.
Time series clustering in large data sets
Directory of Open Access Journals (Sweden)
Jiří Fejfar
2011-01-01
Full Text Available The clustering of time series is a widely researched area. There are many methods for dealing with this task. We are actually using the Self-organizing map (SOM with the unsupervised learning algorithm for clustering of time series. After the first experiment (Fejfar, Weinlichová, Šťastný, 2009 it seems that the whole concept of the clustering algorithm is correct but that we have to perform time series clustering on much larger dataset to obtain more accurate results and to find the correlation between configured parameters and results more precisely. The second requirement arose in a need for a well-defined evaluation of results. It seems useful to use sound recordings as instances of time series again. There are many recordings to use in digital libraries, many interesting features and patterns can be found in this area. We are searching for recordings with the similar development of information density in this experiment. It can be used for musical form investigation, cover songs detection and many others applications.The objective of the presented paper is to compare clustering results made with different parameters of feature vectors and the SOM itself. We are describing time series in a simplistic way evaluating standard deviations for separated parts of recordings. The resulting feature vectors are clustered with the SOM in batch training mode with different topologies varying from few neurons to large maps.There are other algorithms discussed, usable for finding similarities between time series and finally conclusions for further research are presented. We also present an overview of the related actual literature and projects.
The Evolutionary Modeling and Short-range Climatic Prediction for Meteorological Element Time Series
Institute of Scientific and Technical Information of China (English)
YU Kangqing; ZHOU Yuehua; YANG Jing'an; KANG Zhuo
2005-01-01
The time series of precipitation in flood season (May-September) at Wuhan Station, which is set as an example of the kind of time series with chaos characters, is split into two parts: One includes macro climatic timescale period waves that are affected by some relatively steady climatic factors such as astronomical factors (sunspot, etc.), some other known and/or unknown factors, and the other includes micro climatic timescale period waves superimposed on the macro one. The evolutionary modeling (EM), which develops from genetic programming (GP), is supposed to be adept at simulating the former part because it creates the nonlinear ordinary differential equation (NODE) based upon the data series. The natural fractals (NF)are used to simulate the latter part. The final prediction is the sum of results from both methods, thus the model can reflect multi-time scale effects of forcing factors in the climate system. The results of this example for 2002 and 2003 are satisfactory for climatic prediction operation. The NODE can suggest that the data vary with time, which is beneficial to think over short-range climatic analysis and prediction. Comparison in principle between evolutionary modeling and linear modeling indicates that the evolutionary one is a better way to simulate the complex time series with nonlinear characteristics.
Dynamical networks reconstructed from time series
Levnajić, Zoran
2012-01-01
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By statistically examining the correlations between motions displayed by network nodes, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method's implementation on a simple example and discuss the dependence of the reconstruction precision on the properties of time series. Our method is applicable to any network, allowing for reconstruction precision to be maximized, and errors to be estimated.
Improving the prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
李克平; 高自友; 陈天仑
2003-01-01
One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.
Lecture notes for Advanced Time Series Analysis
DEFF Research Database (Denmark)
Madsen, Henrik; Holst, Jan
1997-01-01
A first version of this notes was used at the lectures in Grenoble, and they are now extended and improved (together with Jan Holst), and used in Ph.D. courses on Advanced Time Series Analysis at IMM and at the Department of Mathematical Statistics, University of Lund, 1994, 1997, ......A first version of this notes was used at the lectures in Grenoble, and they are now extended and improved (together with Jan Holst), and used in Ph.D. courses on Advanced Time Series Analysis at IMM and at the Department of Mathematical Statistics, University of Lund, 1994, 1997, ...
Introduction to time series and forecasting
Brockwell, Peter J
2016-01-01
This book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied to economics, engineering and the natural and social sciences. It assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This third edition contains detailed instructions for the use of the professional version of the Windows-based computer package ITSM2000, now available as a free download from the Springer Extras website. The logic and tools of time series model-building are developed in detail. Numerous exercises are included and the software can be used to analyze and forecast data sets of the user's own choosing. The book can also be used in conjunction with other time series packages such as those included in R. The programs in ITSM2000 however are menu-driven and can be used with minimal investment of time in the computational details. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space mod...
Multifractal Analysis of Polyalanines Time Series
Figueirêdo, P H; Moret, M A; Coutinho, Sérgio; 10.1016/j.physa.2009.11.045
2010-01-01
Multifractal properties of the energy time series of short $\\alpha$-helix structures, specifically from a polyalanine family, are investigated through the MF-DFA technique ({\\it{multifractal detrended fluctuation analysis}}). Estimates for the generalized Hurst exponent $h(q)$ and its associated multifractal exponents $\\tau(q)$ are obtained for several series generated by numerical simulations of molecular dynamics in different systems from distinct initial conformations. All simulations were performed using the GROMOS force field, implemented in the program THOR. The main results have shown that all series exhibit multifractal behavior depending on the number of residues and temperature. Moreover, the multifractal spectra reveal important aspects on the time evolution of the system and suggest that the nucleation process of the secondary structures during the visits on the energy hyper-surface is an essential feature of the folding process.
An Assessment of Sunspot Number Data Composites over 1845-2014
Lockwood, M.; Owens, M. J.; Barnard, L.; Usoskin, I. G.
2016-06-01
New sunspot data composites, some of which are radically different in the character of their long-term variation, are evaluated over the interval 1845-2014. The method commonly used to calibrate historic sunspot data, relative to modern-day data, is “daisy-chaining,” whereby calibration is passed from one data subset to the neighboring one, usually using regressions of the data subsets for the intervals of their overlap. Recent studies have illustrated serious pitfalls in these regressions, and the resulting errors can be compounded by their repeated use as the data sequence is extended back in time. Hence, the recent composite data series by Usoskin et al., R UEA, is a very important advance because it avoids regressions, daisy-chaining, and other common, but invalid, assumptions: this is achieved by comparing the statistics of “active-day” fractions to those for a single reference data set. We study six sunspot data series, including R UEA and the new “backbone” data series (R BB, recently generated by Svalgaard & Schatten by employing both regression and daisy-chaining). We show that all six can be used with a continuity model to reproduce the main features of the open solar flux variation for 1845-2014, as reconstructed from geomagnetic activity data. However, some differences can be identified that are consistent with tests using a basket of other proxies for solar magnetic fields. Using data from a variety of sunspot observers, we illustrate problems with the method employed in generating R BB that cause it to increasingly overestimate sunspot numbers going back in time, and we recommend using R UEA because it employs more robust procedures that avoid such problems.
Estimating High-Dimensional Time Series Models
DEFF Research Database (Denmark)
Medeiros, Marcelo C.; Mendes, Eduardo F.
We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume both the number of covariates in the model and candidate variables can increase with the number of observations and the number of candidate variables is, possibly...
Time series tapering for short data samples
DEFF Research Database (Denmark)
Kaimal, J.C.; Kristensen, L.
1991-01-01
We explore the effect of applying tapered windows on atmospheric data to eliminate overestimation inherent in spectra computed from short time series. Some windows are more effective than others in correcting this distortion. The Hamming window gave the best results with experimental data...
Designer networks for time series processing
DEFF Research Database (Denmark)
Svarer, C; Hansen, Lars Kai; Larsen, Jan
1993-01-01
The conventional tapped-delay neural net may be analyzed using statistical methods and the results of such analysis can be applied to model optimization. The authors review and extend efforts to demonstrate the power of this strategy within time series processing. They attempt to design compact...
Lecture notes for Advanced Time Series Analysis
DEFF Research Database (Denmark)
Madsen, Henrik; Holst, Jan
1997-01-01
A first version of this notes was used at the lectures in Grenoble, and they are now extended and improved (together with Jan Holst), and used in Ph.D. courses on Advanced Time Series Analysis at IMM and at the Department of Mathematical Statistics, University of Lund, 1994, 1997, ...
On clustering fMRI time series
DEFF Research Database (Denmark)
Goutte, Cyril; Toft, Peter Aundal; Rostrup, E.
1999-01-01
Analysis of fMRI time series is often performed by extracting one or more parameters for the individual voxels. Methods based, e.g., on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength. However, these methods do...
Optimal transformations for categorical autoregressive time series
Buuren, S. van
1996-01-01
This paper describes a method for finding optimal transformations for analyzing time series by autoregressive models. 'Optimal' implies that the agreement between the autoregressive model and the transformed data is maximal. Such transformations help 1) to increase the model fit, and 2) to analyze c
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Forecasting with periodic autoregressive time series models
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
1999-01-01
textabstractThis paper is concerned with forecasting univariate seasonal time series data using periodic autoregressive models. We show how one should account for unit roots and deterministic terms when generating out-of-sample forecasts. We illustrate the models for various quarterly UK consumption
25 years of time series forecasting
de Gooijer, J.G.; Hyndman, R.J.
2006-01-01
We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985 and International Journal of Forecasting 1985-2005). During
Nonlinear Time Series Analysis via Neural Networks
Volná, Eva; Janošek, Michal; Kocian, Václav; Kotyrba, Martin
This article deals with a time series analysis based on neural networks in order to make an effective forex market [Moore and Roche, J. Int. Econ. 58, 387-411 (2002)] pattern recognition. Our goal is to find and recognize important patterns which repeatedly appear in the market history to adapt our trading system behaviour based on them.
Time Series Rule Discovery: Tough, not Meaningless
Struzik, Z.R.
2003-01-01
`Model free' rule discovery from data has recently been subject to considerable criticism, which has cast a shadow over the emerging discipline of time series data mining. However, other than in data mining, rule discovery has long been the subject of research in statistical physics of complex pheno
25 years of time series forecasting
de Gooijer, J.G.; Hyndman, R.J.
2006-01-01
We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985 and International Journal of Forecasting 1985-2005). During
Parsimonious Linear Fingerprinting for Time Series
2010-09-01
like to detect such groups of harmonics. Fig. 1(d) gives a quick preview of the visualization and effectiveness of the proposed PLiF method: For the...coefficients of each individual frequency. As we find harmonic frequency sets in music , in real time- series like motions, we will expect to usually find
Forecasting with periodic autoregressive time series models
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
1999-01-01
textabstractThis paper is concerned with forecasting univariate seasonal time series data using periodic autoregressive models. We show how one should account for unit roots and deterministic terms when generating out-of-sample forecasts. We illustrate the models for various quarterly UK consumption
On forecasting cointegrated seasonal time series
M. Löf (Marten); Ph.H.B.F. Franses (Philip Hans)
2000-01-01
textabstractWe analyze periodic and seasonal cointegration models for bivariate quarterly observed time series in an empirical forecasting study. We include both single equation and multiple equation methods. A VAR model in first differences with and without cointegration restrictions is also
Efficient Approximate OLAP Querying Over Time Series
DEFF Research Database (Denmark)
Perera, Kasun Baruhupolage Don Kasun Sanjeewa; Hahmann, Martin; Lehner, Wolfgang
2016-01-01
The ongoing trend for data gathering not only produces larger volumes of data, but also increases the variety of recorded data types. Out of these, especially time series, e.g. various sensor readings, have attracted attention in the domains of business intelligence and decision making. As OLAP...
Common large innovations across nonlinear time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2002-01-01
textabstractWe propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as sep
Offset detection in GPS coordinate time series
Gazeaux, J.; King, M. A.; Williams, S. D.
2013-12-01
Global Positioning System (GPS) time series are commonly affected by offsets of unknown magnitude and the large volume of data globally warrants investigation of automated detection approaches. The Detection of Offsets in GPS Experiment (DOGEx) showed that accuracy of Global Positioning System (GPS) time series can be significantly improved by applying statistical offset detection methods (see Gazeaux et al. (2013)). However, the best of these approaches did not perform as well as manual detection by expert analysts. Many of the features of GPS coordinates time series have not yet been fully taken into account in existing methods. Here, we apply Bayesian theory in order to make use of prior knowledge of the site noise characteristics and metadata in an attempt to make the offset detection more accurate. In the past decades, Bayesian theory has shown relevant results for a widespread range of applications, but has not yet been applied to GPS coordinates time series. Such methods incorporate different inputs such as a dynamic model (linear trend, periodic signal..) and a-priori information in a process that provides the best estimate of parameters (velocity, phase and amplitude of periodic signals...) based on all the available information. We test the new method on the DOGEx simulated dataset and compare it to previous solutions, and to Monte-Carlo method to test the accuracy of the procedure. We make a preliminary extension of the DOGEx dataset to introduce metadata information, allowing us to test the value of this data type in detecting offsets. The flexibility, robustness and limitations of the new approach are discussed. Gazeaux, J. Williams, S., King, M., Bos, M., Dach, R., Deo, M.,Moore, A.W., Ostini, L., Petrie, E., Roggero, M., Teferle, F.N., Olivares, G.,Webb, F.H. 2013. Detecting offsets in GPS time series: First results from the detection of offsets in GPS experiment. Journal of Geophysical Research: Solid Earth 118. 5. pp:2169-9356. Keywords : GPS
Horváth, Csilla; Kornelis, Marcel; Leeflang, Peter S.H.
2002-01-01
In this review, we give a comprehensive summary of time series techniques in marketing, and discuss a variety of time series analysis (TSA) techniques and models. We classify them in the sets (i) univariate TSA, (ii) multivariate TSA, and (iii) multiple TSA. We provide relevant marketing application
Horváth, Csilla; Kornelis, Marcel; Leeflang, Peter S.H.
2002-01-01
In this review, we give a comprehensive summary of time series techniques in marketing, and discuss a variety of time series analysis (TSA) techniques and models. We classify them in the sets (i) univariate TSA, (ii) multivariate TSA, and (iii) multiple TSA. We provide relevant marketing application
Horváth, Csilla; Kornelis, Marcel; Leeflang, Peter S.H.
2002-01-01
In this review, we give a comprehensive summary of time series techniques in marketing, and discuss a variety of time series analysis (TSA) techniques and models. We classify them in the sets (i) univariate TSA, (ii) multivariate TSA, and (iii) multiple TSA. We provide relevant marketing
Remote Sensing Time Series Product Tool
Predos, Don; Ryan, Robert E.; Ross, Kenton W.
2006-01-01
The TSPT (Time Series Product Tool) software was custom-designed for NASA to rapidly create and display single-band and band-combination time series, such as NDVI (Normalized Difference Vegetation Index) images, for wide-area crop surveillance and for other time-critical applications. The TSPT, developed in MATLAB, allows users to create and display various MODIS (Moderate Resolution Imaging Spectroradiometer) or simulated VIIRS (Visible/Infrared Imager Radiometer Suite) products as single images, as time series plots at a selected location, or as temporally processed image videos. Manually creating these types of products is extremely labor intensive; however, the TSPT development tool makes the process simplified and efficient. MODIS is ideal for monitoring large crop areas because of its wide swath (2330 km), its relatively small ground sample distance (250 m), and its high temporal revisit time (twice daily). Furthermore, because MODIS imagery is acquired daily, rapid changes in vegetative health can potentially be detected. The new TSPT technology provides users with the ability to temporally process high-revisit-rate satellite imagery, such as that acquired from MODIS and from its successor, the VIIRS. The TSPT features the important capability of fusing data from both MODIS instruments onboard the Terra and Aqua satellites, which drastically improves cloud statistics. With the TSPT, MODIS metadata is used to find and optionally remove bad and suspect data. Noise removal and temporal processing techniques allow users to create low-noise time series plots and image videos and to select settings and thresholds that tailor particular output products. The TSPT GUI (graphical user interface) provides an interactive environment for crafting what-if scenarios by enabling a user to repeat product generation using different settings and thresholds. The TSPT Application Programming Interface provides more fine-tuned control of product generation, allowing experienced
Delay differential analysis of time series.
Lainscsek, Claudia; Sejnowski, Terrence J
2015-03-01
Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time
Delay Differential Analysis of Time Series
Lainscsek, Claudia; Sejnowski, Terrence J.
2015-01-01
Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time
The Statistical Analysis of Time Series
Anderson, T W
2011-01-01
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences George
Outlier Detection in Structural Time Series Models
DEFF Research Database (Denmark)
Marczak, Martyna; Proietti, Tommaso
investigate via Monte Carlo simulations how this approach performs for detecting additive outliers and level shifts in the analysis of nonstationary seasonal time series. The reference model is the basic structural model, featuring a local linear trend, possibly integrated of order two, stochastic seasonality......Structural change affects the estimation of economic signals, like the underlying growth rate or the seasonally adjusted series. An important issue, which has attracted a great deal of attention also in the seasonal adjustment literature, is its detection by an expert procedure. The general...... and a stationary component. Further, we apply both kinds of indicator saturation to detect additive outliers and level shifts in the industrial production series in five European countries....
Nonlinear Analysis of Physiological Time Series
Institute of Scientific and Technical Information of China (English)
MENG Qing-fang; PENG Yu-hua; XUE Yu-li; HAN Min
2007-01-01
Abstract.The heart rate variability could be explained by a low-dimensional governing mechanism. There has been increasing interest in verifying and understanding the coupling between the respiration and the heart rate. In this paper we use the nonlinear detection method to detect the nonlinear deterministic component in the physiological time series by a single variable series and two variables series respectively, and use the conditional information entropy to analyze the correlation between the heart rate, the respiration and the blood oxygen concentration. The conclusions are that there is the nonlinear deterministic component in the heart rate data and respiration data, and the heart rate and the respiration are two variables originating from the same underlying dynamics.
TIME SERIES FORECASTING USING NEURAL NETWORKS
Directory of Open Access Journals (Sweden)
BOGDAN OANCEA
2013-05-01
Full Text Available Recent studies have shown the classification and prediction power of the Neural Networks. It has been demonstrated that a NN can approximate any continuous function. Neural networks have been successfully used for forecasting of financial data series. The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. Neural Networks have the advantage that can approximate nonlinear functions. In this paper we compared the performances of different feed forward and recurrent neural networks and training algorithms for predicting the exchange rate EUR/RON and USD/RON. We used data series with daily exchange rates starting from 2005 until 2013.
Algorithm for Compressing Time-Series Data
Hawkins, S. Edward, III; Darlington, Edward Hugo
2012-01-01
An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").
Pseudotime estimation: deconfounding single cell time series.
Reid, John E; Wernisch, Lorenz
2016-10-01
Repeated cross-sectional time series single cell data confound several sources of variation, with contributions from measurement noise, stochastic cell-to-cell variation and cell progression at different rates. Time series from single cell assays are particularly susceptible to confounding as the measurements are not averaged over populations of cells. When several genes are assayed in parallel these effects can be estimated and corrected for under certain smoothness assumptions on cell progression. We present a principled probabilistic model with a Bayesian inference scheme to analyse such data. We demonstrate our method's utility on public microarray, nCounter and RNA-seq datasets from three organisms. Our method almost perfectly recovers withheld capture times in an Arabidopsis dataset, it accurately estimates cell cycle peak times in a human prostate cancer cell line and it correctly identifies two precocious cells in a study of paracrine signalling in mouse dendritic cells. Furthermore, our method compares favourably with Monocle, a state-of-the-art technique. We also show using held-out data that uncertainty in the temporal dimension is a common confounder and should be accounted for in analyses of repeated cross-sectional time series. Our method is available on CRAN in the DeLorean package. john.reid@mrc-bsu.cam.ac.uk Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.
Hurst exponents for short time series
Qi, Jingchao; Yang, Huijie
2011-12-01
A concept called balanced estimator of diffusion entropy is proposed to detect quantitatively scalings in short time series. The effectiveness is verified by detecting successfully scaling properties for a large number of artificial fractional Brownian motions. Calculations show that this method can give reliable scalings for short time series with length ˜102. It is also used to detect scalings in the Shanghai Stock Index, five stock catalogs, and a total of 134 stocks collected from the Shanghai Stock Exchange Market. The scaling exponent for each catalog is significantly larger compared with that for the stocks included in the catalog. Selecting a window with size 650, the evolution of scaling for the Shanghai Stock Index is obtained by the window's sliding along the series. Global patterns in the evolutionary process are captured from the smoothed evolutionary curve. By comparing the patterns with the important event list in the history of the considered stock market, the evolution of scaling is matched with the stock index series. We can find that the important events fit very well with global transitions of the scaling behaviors.
Univariate time series forecasting algorithm validation
Ismail, Suzilah; Zakaria, Rohaiza; Muda, Tuan Zalizam Tuan
2014-12-01
Forecasting is a complex process which requires expert tacit knowledge in producing accurate forecast values. This complexity contributes to the gaps between end users and expert. Automating this process by using algorithm can act as a bridge between them. Algorithm is a well-defined rule for solving a problem. In this study a univariate time series forecasting algorithm was developed in JAVA and validated using SPSS and Excel. Two set of simulated data (yearly and non-yearly); several univariate forecasting techniques (i.e. Moving Average, Decomposition, Exponential Smoothing, Time Series Regressions and ARIMA) and recent forecasting process (such as data partition, several error measures, recursive evaluation and etc.) were employed. Successfully, the results of the algorithm tally with the results of SPSS and Excel. This algorithm will not just benefit forecaster but also end users that lacking in depth knowledge of forecasting process.
Time-Series Analysis: A Cautionary Tale
Damadeo, Robert
2015-01-01
Time-series analysis has often been a useful tool in atmospheric science for deriving long-term trends in various atmospherically important parameters (e.g., temperature or the concentration of trace gas species). In particular, time-series analysis has been repeatedly applied to satellite datasets in order to derive the long-term trends in stratospheric ozone, which is a critical atmospheric constituent. However, many of the potential pitfalls relating to the non-uniform sampling of the datasets were often ignored and the results presented by the scientific community have been unknowingly biased. A newly developed and more robust application of this technique is applied to the Stratospheric Aerosol and Gas Experiment (SAGE) II version 7.0 ozone dataset and the previous biases and newly derived trends are presented.
Multivariate Voronoi Outlier Detection for Time Series.
Zwilling, Chris E; Wang, Michelle Yongmei
2014-10-01
Outlier detection is a primary step in many data mining and analysis applications, including healthcare and medical research. This paper presents a general method to identify outliers in multivariate time series based on a Voronoi diagram, which we call Multivariate Voronoi Outlier Detection (MVOD). The approach copes with outliers in a multivariate framework, via designing and extracting effective attributes or features from the data that can take parametric or nonparametric forms. Voronoi diagrams allow for automatic configuration of the neighborhood relationship of the data points, which facilitates the differentiation of outliers and non-outliers. Experimental evaluation demonstrates that our MVOD is an accurate, sensitive, and robust method for detecting outliers in multivariate time series data.
Visibility graphlet approach to chaotic time series
Energy Technology Data Exchange (ETDEWEB)
Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2016-05-15
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Visibility graphlet approach to chaotic time series.
Mutua, Stephen; Gu, Changgui; Yang, Huijie
2016-05-01
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Inductorless Chua's Circuit: Experimental Time Series Analysis
Directory of Open Access Journals (Sweden)
R. M. Rubinger
2007-01-01
Full Text Available We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor R as the control parameter and varying from 1300 Ω to 2000 Ω. Experimental time series at fixed R were used to reconstruct attractors by the delay vector technique. The flow attractors and their Poincaré maps considering parameters such as the Lyapunov spectrum, its subproduct the Kaplan-Yorke dimension, and the information dimension are also analyzed here. The results for a typical double scroll attractor indicate a chaotic behavior characterized by a positive Lyapunov exponent and with a Kaplan-Yorke dimension of 2.14. The occurrence of chaos was also investigated through numerical simulations of the Chua's circuit set of differential equations.
On clustering fMRI time series
DEFF Research Database (Denmark)
Goutte, C; Toft, P; Rostrup, E
1999-01-01
Analysis of fMRI time series is often performed by extracting one or more parameters for the individual voxels. Methods based, e.g., on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength. However, these methods do not indi......Analysis of fMRI time series is often performed by extracting one or more parameters for the individual voxels. Methods based, e.g., on various statistical tests are then used to yield parameters corresponding to probability of activation or activation strength. However, these methods do...... between the activation stimulus and the fMRI signal. We present two different clustering algorithms and use them to identify regions of similar activations in an fMRI experiment involving a visual stimulus....
Learning and Prediction of Relational Time Series
2013-03-01
genetic algorithms can generate a sequence of events to maximize some functions or the likelihood to achieve the assumed goals. With reference...Reinforcement learning is not the same as relational time-series learning mainly because its main focus is to learn a set of policies to maximize the...scope blending, and has been applied to machine poetry generation [48] and the generation of animation characters [49]. Tan and Kowk [50] applied the
Revisiting algorithms for generating surrogate time series
Raeth, C; Papadakis, I E; Brinkmann, W
2011-01-01
The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to non-detections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.
Time Series Modelling using Proc Varmax
DEFF Research Database (Denmark)
Milhøj, Anders
2007-01-01
In this paper it will be demonstrated how various time series problems could be met using Proc Varmax. The procedure is rather new and hence new features like cointegration, testing for Granger causality are included, but it also means that more traditional ARIMA modelling as outlined by Box & Je...... & Jenkins is performed in a more modern way using the computer resources which are now available...
COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY
Energy Technology Data Exchange (ETDEWEB)
Deng, L. H.; Xiang, Y. Y.; Dun, G. T. [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216 (China); Li, B., E-mail: wooden@escience.cn [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, Weihai 264209 (China)
2016-01-15
The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.
Comparison of Chaotic and Fractal Properties of Polar Faculae with Sunspot Activity
Deng, L. H.; Li, B.; Xiang, Y. Y.; Dun, G. T.
2016-01-01
The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock-Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.
Normalizing the causality between time series
Liang, X San
2015-01-01
Recently, a rigorous yet concise formula has been derived to evaluate the information flow, and hence the causality in a quantitative sense, between time series. To assess the importance of a resulting causality, it needs to be normalized. The normalization is achieved through distinguishing three types of fundamental mechanisms that govern the marginal entropy change of the flow recipient. A normalized or relative flow measures its importance relative to other mechanisms. In analyzing realistic series, both absolute and relative information flows need to be taken into account, since the normalizers for a pair of reverse flows belong to two different entropy balances; it is quite normal that two identical flows may differ a lot in relative importance in their respective balances. We have reproduced these results with several autoregressive models. We have also shown applications to a climate change problem and a financial analysis problem. For the former, reconfirmed is the role of the Indian Ocean Dipole as ...
Jiang, Jie; Schmitt, Dieter; Schuessler, Manfred
2011-01-01
We use the historic record of sunspot groups compiled by the Royal Greenwich Observatory together with the sunspot number to derive the statistical properties of sunspot group emergence in dependence of cycle phase and strength. In particular we discuss the latitude, longitude, area and tilt angle of sunspot groups as functions of the cycle strength and of time during the solar cycle. Using these empirical characteristics the time-latitude diagram of sunspot group emergence (butterfly diagram) is reconstructed from 1700 onward on the basis of the Wolf and group sunspot numbers. This reconstruction will be useful in studies of the long-term evolution of the Sun's magnetic field.
Argos: An Optimized Time-Series Photometer
Indian Academy of Sciences (India)
Anjum S. Mukadam; R. E. Nather
2005-06-01
We designed a prime focus CCD photometer, Argos, optimized for high speed time-series measurements of blue variables (Nather & Mukadam 2004) for the 2.1 m telescope at McDonald Observatory. Lack of any intervening optics between the primary mirror and the CCD makes the instrument highly efficient.We measure an improvement in sensitivity by a factor of nine over the 3-channel PMT photometers used on the same telescope and for the same exposure time. The CCD frame transfer operation triggered by GPS synchronized pulses serves as an electronic shutter for the photometer. This minimizes the dead time between exposures, but more importantly, allows a precise control of the start and duration of the exposure. We expect the uncertainty in our timing to be less than 100 s.
Directed networks with underlying time structures from multivariate time series
Tanizawa, Toshihiro; Taya, Fumihiko
2014-01-01
In this paper we propose a method of constructing directed networks of time-dependent phenomena from multivariate time series. As the construction method is based on the linear model, the network fully reflects dynamical features of the system such as time structures of periodicities. Furthermore, this method can construct networks even if these time series show no similarity: situations in which common methods fail. We explicitly introduce a case where common methods do not work. This fact indicates the importance of constructing networks based on dynamical perspective, when we consider time-dependent phenomena. We apply the method to multichannel electroencephalography~(EEG) data and the result reveals underlying interdependency among the components in the brain system.
Fractal fluctuations in cardiac time series
West, B. J.; Zhang, R.; Sanders, A. W.; Miniyar, S.; Zuckerman, J. H.; Levine, B. D.; Blomqvist, C. G. (Principal Investigator)
1999-01-01
Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.
Time Series Photometry of KZ Lacertae
Joner, Michael D.
2016-01-01
We present BVRI time series photometry of the high amplitude delta Scuti star KZ Lacertae secured using the 0.9-meter telescope located at the Brigham Young University West Mountain Observatory. In addition to the multicolor light curves that are presented, the V data from the last six years of observations are used to plot an O-C diagram in order to determine the ephemeris and evaluate evidence for period change. We wish to thank the Brigham Young University College of Physical and Mathematical Sciences as well as the Department of Physics and Astronomy for their continued support of the research activities at the West Mountain Observatory.
Fourier analysis of time series an introduction
Bloomfield, Peter
2000-01-01
A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...
Modeling noisy time series Physiological tremor
Timmer, J
1998-01-01
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the outstretched hand of healthy subjects, we compare the results for a linear model that explicitly includes additional observational noise to one that ignores this noise. We discuss problems and possible solutions for nonlinear deterministic as well as nonlinear stochastic processes. Especially we discuss the state space model applicable for modeling noisy stochastic systems and Bock's algorithm capable for modeling noisy deterministic systems.
Time series modeling for automatic target recognition
Sokolnikov, Andre
2012-05-01
Time series modeling is proposed for identification of targets whose images are not clearly seen. The model building takes into account air turbulence, precipitation, fog, smoke and other factors obscuring and distorting the image. The complex of library data (of images, etc.) serving as a basis for identification provides the deterministic part of the identification process, while the partial image features, distorted parts, irrelevant pieces and absence of particular features comprise the stochastic part of the target identification. The missing data approach is elaborated that helps the prediction process for the image creation or reconstruction. The results are provided.
Time Series Analysis of SOLSTICE Measurements
Wen, G.; Cahalan, R. F.
2003-12-01
Solar radiation is the major energy source for the Earth's biosphere and atmospheric and ocean circulations. Variations of solar irradiance have been a major concern of scientists both in solar physics and atmospheric sciences. A number of missions have been carried out to monitor changes in total solar irradiance (TSI) [see Fröhlich and Lean, 1998 for review] and spectral solar irradiance (SSI) [e.g., SOLSTICE on UARS and VIRGO on SOHO]. Observations over a long time period reveal the connection between variations in solar irradiance and surface magnetic fields of the Sun [Lean1997]. This connection provides a guide to scientists in modeling solar irradiances [e.g., Fontenla et al., 1999; Krivova et al., 2003]. Solar spectral observations have now been made over a relatively long time period, allowing statistical analysis. This paper focuses on predictability of solar spectral irradiance using observed SSI from SOLSTICE . Analysis of predictability is based on nonlinear dynamics using an artificial neural network in a reconstructed phase space [Abarbanel et al., 1993]. In the analysis, we first examine the average mutual information of the observed time series and a delayed time series. The time delay that gives local minimum of mutual information is chosen as the time-delay for phase space reconstruction [Fraser and Swinney, 1986]. The embedding dimension of the reconstructed phase space is determined using the false neighbors and false strands method [Kennel and Abarbanel, 2002]. Subsequently, we use a multi-layer feed-forward network with back propagation scheme [e.g., Haykin, 1994] to model the time series. The predictability of solar irradiance as a function of wavelength is considered. References Abarbanel, H. D. I., R. Brown, J. J. Sidorowich, and L. Sh. Tsimring, Rev. Mod. Phys. 65, 1331, 1993. Fraser, A. M. and H. L. Swinney, Phys. Rev. 33A, 1134, 1986. Fontenla, J., O. R. White, P. Fox, E. H. Avrett and R. L. Kurucz, The Astrophysical Journal, 518, 480
An introduction to state space time series analysis.
Commandeur, J.J.F. & Koopman, S.J.
2007-01-01
Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor wi
Nonlinear Time Series Analysis Since 1990:Some Personal Reflections
Institute of Scientific and Technical Information of China (English)
Howel Tong
2002-01-01
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
Ensemble vs. time averages in financial time series analysis
Seemann, Lars; Hua, Jia-Chen; McCauley, Joseph L.; Gunaratne, Gemunu H.
2012-12-01
Empirical analysis of financial time series suggests that the underlying stochastic dynamics are not only non-stationary, but also exhibit non-stationary increments. However, financial time series are commonly analyzed using the sliding interval technique that assumes stationary increments. We propose an alternative approach that is based on an ensemble over trading days. To determine the effects of time averaging techniques on analysis outcomes, we create an intraday activity model that exhibits periodic variable diffusion dynamics and we assess the model data using both ensemble and time averaging techniques. We find that ensemble averaging techniques detect the underlying dynamics correctly, whereas sliding intervals approaches fail. As many traded assets exhibit characteristic intraday volatility patterns, our work implies that ensemble averages approaches will yield new insight into the study of financial markets’ dynamics.
Partial spectral analysis of hydrological time series
Jukić, D.; Denić-Jukić, V.
2011-03-01
SummaryHydrological time series comprise the influences of numerous processes involved in the transfer of water in hydrological cycle. It implies that an ambiguity with respect to the processes encoded in spectral and cross-spectral density functions exists. Previous studies have not paid attention adequately to this issue. Spectral and cross-spectral density functions represent the Fourier transforms of auto-covariance and cross-covariance functions. Using this basic property, the ambiguity is resolved by applying a novel approach based on the spectral representation of partial correlation. Mathematical background for partial spectral density, partial amplitude and partial phase functions is presented. The proposed functions yield the estimates of spectral density, amplitude and phase that are not affected by a controlling process. If an input-output relation is the subject of interest, antecedent and subsequent influences of the controlling process can be distinguished considering the input event as a referent point. The method is used for analyses of the relations between the rainfall, air temperature and relative humidity, as well as the influences of air temperature and relative humidity on the discharge from karst spring. Time series are collected in the catchment of the Jadro Spring located in the Dinaric karst area of Croatia.
Lockwood, M.; Owens, M. J.; Barnard, L.
2016-11-01
We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group-number data sequences. The data series tested are the original and new versions of the Wolf/Zürich/International sunspot number composite [R_{{ISNv1}} and R_{{ISNv2}}] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of R ISNv1 proposed by Lockwood, Owens, and Barnard ( J. Geophys. Res. 119, 5193, 2014a) [R C]; the new "backbone" group-number composite proposed by Svalgaard and Schatten ( Solar Phys. 291, 2016) [R_{{BB}}]; and the new group-number composite derived by Usoskin et al. ( Solar Phys. 291, 2016) [R_{{UEA}}]. The test data series used are the group-number [NG] and total sunspot area [A G] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the sunspot-group-number from the MWO sunspot drawings [N_{{MWO}}]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, R_{BB}, and R_{{ISNv1}}, but not by R_{{ISNv2}} or R_{{UEA}}. The five test datasets give very similar results in all cases. By multiplying the probability
Forecasting autoregressive time series under changing persistence
DEFF Research Database (Denmark)
Kruse, Robinson
Changing persistence in time series models means that a structural change from nonstationarity to stationarity or vice versa occurs over time. Such a change has important implications for forecasting, as negligence may lead to inaccurate model predictions. This paper derives generally applicable...... recommendations, no matter whether a change in persistence occurs or not. Seven different forecasting strategies based on a biasedcorrected estimator are compared by means of a large-scale Monte Carlo study. The results for decreasing and increasing persistence are highly asymmetric and new to the literature. Its...... good predictive ability and its balanced performance among different settings strongly advocate the use of forecasting strategies based on the Bai-Perron procedure....
Useful Pattern Mining on Time Series
DEFF Research Database (Denmark)
Goumatianos, Nikitas; Christou, Ioannis T; Lindgren, Peter
2013-01-01
We present the architecture of a “useful pattern” mining system that is capable of detecting thousands of different candlestick sequence patterns at the tick or any higher granularity levels. The system architecture is highly distributed and performs most of its highly compute-intensive aggregation...... calculations as complex but efficient distributed SQL queries on the relational databases that store the time-series. We present initial results from mining all frequent candlestick sequences with the characteristic property that when they occur then, with an average at least 60% probability, they signal a 2......% or higher increase (or, alternatively, decrease) in a chosen property of the stock (e.g. close-value) within a given time-window (e.g. 5 days). Initial results from a first prototype implementation of the architecture show that after training on a large set of stocks, the system is capable of finding...
Learning with Latent Factors in Time Series
Jalali, Ali
2011-01-01
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some variables, and never observe other variables; from this, we would like to find the dependency structure between the observed variables -- separating out the spurious interactions caused by the (marginalizing out of the) latent variables' time series. We develop a new method, based on convex optimization, to do so in the case when the number of latent variables is smaller than the number of observed ones. For the case when the dependency structure between the observed variables is sparse, we theoretically establish a high-dimensional scaling result for structure recovery. We verify our theoretical result with both synthetic and real data (from the stock market).
Automated time series forecasting for biosurveillance.
Burkom, Howard S; Murphy, Sean Patrick; Shmueli, Galit
2007-09-30
For robust detection performance, traditional control chart monitoring for biosurveillance is based on input data free of trends, day-of-week effects, and other systematic behaviour. Time series forecasting methods may be used to remove this behaviour by subtracting forecasts from observations to form residuals for algorithmic input. We describe three forecast methods and compare their predictive accuracy on each of 16 authentic syndromic data streams. The methods are (1) a non-adaptive regression model using a long historical baseline, (2) an adaptive regression model with a shorter, sliding baseline, and (3) the Holt-Winters method for generalized exponential smoothing. Criteria for comparing the forecasts were the root-mean-square error, the median absolute per cent error (MedAPE), and the median absolute deviation. The median-based criteria showed best overall performance for the Holt-Winters method. The MedAPE measures over the 16 test series averaged 16.5, 11.6, and 9.7 for the non-adaptive regression, adaptive regression, and Holt-Winters methods, respectively. The non-adaptive regression forecasts were degraded by changes in the data behaviour in the fixed baseline period used to compute model coefficients. The mean-based criterion was less conclusive because of the effects of poor forecasts on a small number of calendar holidays. The Holt-Winters method was also most effective at removing serial autocorrelation, with most 1-day-lag autocorrelation coefficients below 0.15. The forecast methods were compared without tuning them to the behaviour of individual series. We achieved improved predictions with such tuning of the Holt-Winters method, but practical use of such improvements for routine surveillance will require reliable data classification methods.
Trend prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Trend prediction of chaotic ti me series is anin-teresting probleminti me series analysis andti me se-ries data mining(TSDM)fields[1].TSDM-basedmethods can successfully characterize and predictcomplex,irregular,and chaotic ti me series.Somemethods have been proposed to predict the trend ofchaotic ti me series.In our knowledge,these meth-ods can be classified into t wo categories as follows.The first category is based on the embeddedspace[2-3],where rawti me series data is mapped to areconstructed phase spac...
A New SBUV Ozone Profile Time Series
McPeters, Richard
2011-01-01
Under NASA's MEaSUREs program for creating long term multi-instrument data sets, our group at Goddard has re-processed ozone profile data from a series of SBUV instruments. We have processed data from the Nimbus 7 SBUV instrument (1979-1990) and data from SBUV/2 instruments on NOAA-9 (1985-1998), NOAA-11 (1989-1995), NOAA-16 (2001-2010), NOAA-17 (2002-2010), and NOAA-18 (2005-2010). This reprocessing uses the version 8 ozone profile algorithm but now uses the Brion, Daumont, and Malicet (BMD) ozone cross sections instead of the Bass and Paur cross sections. The new cross sections have much better resolution, and extended wavelength range, and a more consistent temperature dependence. The re-processing also uses an improved cloud height climatology based on the Raman cloud retrievals of OMI. Finally, the instrument-to-instrument calibration is set using matched scenes so that ozone diurnal variation in the upper stratosphere does not alias into the ozone trands. Where there is no instrument overlap, SAGE and MLS are used to estimate calibration offsets. Preliminary analysis shows a more coherent time series as a function of altitude. The net effect on profile total column ozone is on average an absolute reduction of about one percent. Comparisons with ground-based systems are significantly better at high latitudes.
Correcting and combining time series forecasters.
Firmino, Paulo Renato A; de Mattos Neto, Paulo S G; Ferreira, Tiago A E
2014-02-01
Combined forecasters have been in the vanguard of stochastic time series modeling. In this way it has been usual to suppose that each single model generates a residual or prediction error like a white noise. However, mostly because of disturbances not captured by each model, it is yet possible that such supposition is violated. The present paper introduces a two-step method for correcting and combining forecasting models. Firstly, the stochastic process underlying the bias of each predictive model is built according to a recursive ARIMA algorithm in order to achieve a white noise behavior. At each iteration of the algorithm the best ARIMA adjustment is determined according to a given information criterion (e.g. Akaike). Then, in the light of the corrected predictions, it is considered a maximum likelihood combined estimator. Applications involving single ARIMA and artificial neural networks models for Dow Jones Industrial Average Index, S&P500 Index, Google Stock Value, and Nasdaq Index series illustrate the usefulness of the proposed framework.
Periodograms for multiband astronomical time series
Ivezic, Z.; VanderPlas, J. T.
2016-05-01
We summarize the multiband periodogram, a general extension of the well-known Lomb-Scargle approach for detecting periodic signals in time- domain data developed by VanderPlas & Ivezic (2015). A Python implementation of this method is available on GitHub. The multiband periodogram significantly improves period finding for randomly sampled multiband light curves (e.g., Pan-STARRS, DES, and LSST), and can treat non-uniform sampling and heteroscedastic errors. The light curves in each band are modeled as arbitrary truncated Fourier series, with the period and phase shared across all bands. The key aspect is the use of Tikhonov regularization which drives most of the variability into the so-called base model common to all bands, while fits for individual bands describe residuals relative to the base model and typically require lower-order Fourier series. We use simulated light curves and randomly subsampled SDSS Stripe 82 data to demonstrate the superiority of this method compared to other methods from the literature, and find that this method will be able to efficiently determine the correct period in the majority of LSST's bright RR Lyrae stars with as little as six months of LSST data.
Novel FTLRNN with Gamma Memory for Short-Term and Long-Term Predictions of Chaotic Time Series
Directory of Open Access Journals (Sweden)
Sanjay L. Badjate
2009-01-01
Full Text Available Multistep ahead prediction of a chaotic time series is a difficult task that has attracted increasing interest in the recent years. The interest in this work is the development of nonlinear neural network models for the purpose of building multistep chaotic time series prediction. In the literature there is a wide range of different approaches but their success depends on the predicting performance of the individual methods. Also the most popular neural models are based on the statistical and traditional feed forward neural networks. But it is seen that this kind of neural model may present some disadvantages when long-term prediction is required. In this paper focused time-lagged recurrent neural network (FTLRNN model with gamma memory is developed for different prediction horizons. It is observed that this predictor performs remarkably well for short-term predictions as well as medium-term predictions. For coupled partial differential equations generated chaotic time series such as Mackey Glass and Duffing, FTLRNN-based predictor performs consistently well for different depths of predictions ranging from short term to long term, with only slight deterioration after k is increased beyond 50. For real-world highly complex and nonstationary time series like Sunspots and Laser, though the proposed predictor does perform reasonably for short term and medium-term predictions, its prediction ability drops for long term ahead prediction. However, still this is the best possible prediction results considering the facts that these are nonstationary time series. As a matter of fact, no other NN configuration can match the performance of FTLRNN model. The authors experimented the performance of this FTLRNN model on predicting the dynamic behavior of typical Chaotic Mackey-Glass time series, Duffing time series, and two real-time chaotic time series such as monthly sunspots and laser. Static multi layer perceptron (MLP model is also attempted and compared
Normalizing the causality between time series
Liang, X. San
2015-08-01
Recently, a rigorous yet concise formula was derived to evaluate information flow, and hence the causality in a quantitative sense, between time series. To assess the importance of a resulting causality, it needs to be normalized. The normalization is achieved through distinguishing a Lyapunov exponent-like, one-dimensional phase-space stretching rate and a noise-to-signal ratio from the rate of information flow in the balance of the marginal entropy evolution of the flow recipient. It is verified with autoregressive models and applied to a real financial analysis problem. An unusually strong one-way causality is identified from IBM (International Business Machines Corporation) to GE (General Electric Company) in their early era, revealing to us an old story, which has almost faded into oblivion, about "Seven Dwarfs" competing with a giant for the mainframe computer market.
Inferring causality from noisy time series data
DEFF Research Database (Denmark)
Mønster, Dan; Fusaroli, Riccardo; Tylén, Kristian;
2016-01-01
Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We find that CCM fails to infer accurate coupling strength...... and even causality direction in synchronized time-series and in the presence of intermediate coupling. We find that the presence of noise deterministically reduces the level of cross-mapping fidelity, while the convergence rate exhibits higher levels of robustness. Finally, we propose that controlled noise...... injections in intermediate-to-strongly coupled systems could enable more accurate causal inferences. Given the inherent noisy nature of real-world systems, our findings enable a more accurate evaluation of CCM applicability and advance suggestions on how to overcome its weaknesses....
An Assessment of Sunspot Number Data Composites over 1845-2014
Lockwood, Mike; Barnard, Luke A; Usoskin, Ilya G
2016-01-01
New sunspot data composites, some of which are radically different in the character of their long-term variation, are evaluated over the interval 1845-2014. The method commonly used to calibrate historic sunspot data, relative to modern-day data, is "daisy-chaining", whereby calibration is passed from one data subset to the neighbouring one, usually using regressions of the data subsets for the intervals of their overlap. Recent studies have illustrated serious pitfalls in these regressions and the resulting errors can be compounded by their repeated use as the data sequence is extended back in time. Hence the recent composite data series by Usoskin et al. (2016), $R_{UEA}$, is a very important advance because it avoids regressions, daisy-chaining and other common, but invalid, assumptions: this is achieved by comparing the statistics of "active day" fractions to those for a single reference dataset. We study six sunspot data series including $R_{UEA}$ and the new "backbone" data series $R_{BB}$, recently gen...
Sunspot Group Development in High Resolution
Muraközy, J; Ludmány, A
2014-01-01
The Solar and Heliospheric Obseratory/Michelson Doppler Imager--Debrecen Data (SDD) sunspot catalogue provides an opportunity to study the details and development of sunspot groups on a large statistical sample. The SDD data allow, in particular, the differential study of the leading and following parts with a temporal resolution of 1.5 hours. In this study, we analyse the equilibrium distance of sunspot groups as well as the evolution of this distance over the lifetime of the groups and the shifts in longitude associated with these groups. We also study the asymmetry between the compactness of the leading and following parts, as well as the time-profiles for the development of the area of sunspot groups. A logarithmic relationship has been found between the total area and the distance of leading-following parts of active regions (ARs) at the time of their maximum area. In the developing phase the leading part moves forward; this is more noticeable in larger ARs. The leading part has a higher growth rate than...
Highly comparative, feature-based time-series classification
Fulcher, Ben D
2014-01-01
A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across the scientific time-series analysis literature, and include summaries of time series in terms of their correlation structure, distribution, entropy, stationarity, scaling properties, and fits to a range of time-series models. After computing thousands of features for each time series in a training set, those that are most informative of the class structure are selected using greedy forward feature selection with a linear classifier. The resulting feature-based classifiers automatically learn the differences between classes using a reduced number of time-series properties, and circumvent the need to calculate distances between time series. Representing time series in this way results in orders of magnitude of dimensionality reduction, allowing the method to perform well on ve...
PERIODOGRAMS FOR MULTIBAND ASTRONOMICAL TIME SERIES
Energy Technology Data Exchange (ETDEWEB)
VanderPlas, Jacob T. [eScience Institute, University of Washington, Seattle, WA (United States); Ivezic, Željko [Department of Astronomy, University of Washington, Seattle, WA (United States)
2015-10-10
This paper introduces the multiband periodogram, a general extension of the well-known Lomb–Scargle approach for detecting periodic signals in time-domain data. In addition to advantages of the Lomb–Scargle method such as treatment of non-uniform sampling and heteroscedastic errors, the multiband periodogram significantly improves period finding for randomly sampled multiband light curves (e.g., Pan-STARRS, DES, and LSST). The light curves in each band are modeled as arbitrary truncated Fourier series, with the period and phase shared across all bands. The key aspect is the use of Tikhonov regularization which drives most of the variability into the so-called base model common to all bands, while fits for individual bands describe residuals relative to the base model and typically require lower-order Fourier series. This decrease in the effective model complexity is the main reason for improved performance. After a pedagogical development of the formalism of least-squares spectral analysis, which motivates the essential features of the multiband model, we use simulated light curves and randomly subsampled SDSS Stripe 82 data to demonstrate the superiority of this method compared to other methods from the literature and find that this method will be able to efficiently determine the correct period in the majority of LSST’s bright RR Lyrae stars with as little as six months of LSST data, a vast improvement over the years of data reported to be required by previous studies. A Python implementation of this method, along with code to fully reproduce the results reported here, is available on GitHub.
Nature's third cycle a story of sunspots
Choudhuri, Arnab Rai
2015-01-01
The cycle of day and night and the cycle of seasons are two familiar natural cycles around which many human activities are organized. But is there a third natural cycle of importance for us humans? On 13 March 1989, six million people in Canada went without electricity for many hours: a large explosion on the sun was discovered as the cause of this blackout. Such explosions occur above sunspots, dark features on the surface of the Sun that have been observed through telescopes since the time of Galileo. The number of sunspots has been found to wax and wane over a period of 11 years. Although this cycle was discovered less than two centuries ago, it is becoming increasingly important for us as human society becomes more dependent on technology. For nearly a century after its discovery, the cause of the sunspot cycle remained completely shrouded in mystery. The 1908 discovery of strong magnetic fields in sunspots made it clear that the 11-year cycle is the magnetic cycle of the sun. It is only during the last ...
Eichelberger, Hans; Schwingenschuh, Konrad; Besser, B. P.; Prattes, Gustav; Aydogar; Wolbang, Daniel; Rozhnoi, Alexander; Solovieva, Maria; Biagi, Pier Francesco; Boudjada, Mohammed
2016-07-01
We focus on natural disturbances of the sub-ionospheric VLF waveguide in the time span 2009 to 2015 (sunspot cycle 24), i.e. variations in amplitude and phase measurements of the radio paths are considered. In particular we're investigating numerous solar flares (up to X-class), geomagnetic storms and substorms, therefore discuss how to discriminate natural from artificial variations between different transmitters and receivers. Meteorological effects could be important [1] and we estimate the possibility to detect the influence of lithospheric sources in the VLF radio links. As part of the VLF multistation network we're using the single receiver mid-latitude station in Graz, Austria. This facility receives up to 12 transmitter simultaneously (frequency range 10-50 kHz), has 20 sec temporal resolution, and is running continuously since 2009 [2]. We obtain the statistics relating VLF amplitude and phase fluctuations with C/M/X-class solar flares, and characterise night time fluctuations in connection with enhanced particle precipitation in the northern latitude path (Iceland transmitter). The statistics is important to improve the quality of seismo-electromagnetic studies. We conclude that for ionospheric perturbations (D-layer), e.g. solar flares, a reliable real time monitoring service can be established. Atmospheric and lithospheric variations are generally difficult to characterise, it's harder to distinguish between natural and man made signals, therefore - as a future outlook - complementary ground and satellite based measurements can deliver valuable additional information for environmental monitoring. References: [1] A. Rozhnoi et al.: Meteorological effects in the lower ionosphere as based on VLF/LF signal observations, Nat. Hazards Earth Syst. Sci., 14, 2671-2679, 2014. [2] K. Schwingenschuh et al.: The Graz seismo-electromagnetic VLF facility, Nat. Hazards Earth Syst. Sci., 11, 1121-1127, 2011.
Timing calibration and spectral cleaning of LOFAR time series data
Corstanje, A.; Buitink, S.; Enriquez, J. E.; Falcke, H.; Hörandel, J. R.; Krause, M.; Nelles, A.; Rachen, J. P.; Schellart, P.; Scholten, O.; ter Veen, S.; Thoudam, S.; Trinh, T. N. G.
2016-05-01
We describe a method for spectral cleaning and timing calibration of short time series data of the voltage in individual radio interferometer receivers. It makes use of phase differences in fast Fourier transform (FFT) spectra across antenna pairs. For strong, localized terrestrial sources these are stable over time, while being approximately uniform-random for a sum over many sources or for noise. Using only milliseconds-long datasets, the method finds the strongest interfering transmitters, a first-order solution for relative timing calibrations, and faulty data channels. No knowledge of gain response or quiescent noise levels of the receivers is required. With relatively small data volumes, this approach is suitable for use in an online system monitoring setup for interferometric arrays. We have applied the method to our cosmic-ray data collection, a collection of measurements of short pulses from extensive air showers, recorded by the LOFAR radio telescope. Per air shower, we have collected 2 ms of raw time series data for each receiver. The spectral cleaning has a calculated optimal sensitivity corresponding to a power signal-to-noise ratio of 0.08 (or -11 dB) in a spectral window of 25 kHz, for 2 ms of data in 48 antennas. This is well sufficient for our application. Timing calibration across individual antenna pairs has been performed at 0.4 ns precision; for calibration of signal clocks across stations of 48 antennas the precision is 0.1 ns. Monitoring differences in timing calibration per antenna pair over the course of the period 2011 to 2015 shows a precision of 0.08 ns, which is useful for monitoring and correcting drifts in signal path synchronizations. A cross-check method for timing calibration is presented, using a pulse transmitter carried by a drone flying over the array. Timing precision is similar, 0.3 ns, but is limited by transmitter position measurements, while requiring dedicated flights.
Timing calibration and spectral cleaning of LOFAR time series data
Corstanje, A; Enriquez, J E; Falcke, H; Hörandel, J R; Krause, M; Nelles, A; Rachen, J P; Schellart, P; Scholten, O; ter Veen, S; Thoudam, S; Trinh, T N G
2016-01-01
We describe a method for spectral cleaning and timing calibration of short voltage time series data from individual radio interferometer receivers. It makes use of the phase differences in Fast Fourier Transform (FFT) spectra across antenna pairs. For strong, localized terrestrial sources these are stable over time, while being approximately uniform-random for a sum over many sources or for noise. Using only milliseconds-long datasets, the method finds the strongest interfering transmitters, a first-order solution for relative timing calibrations, and faulty data channels. No knowledge of gain response or quiescent noise levels of the receivers is required. With relatively small data volumes, this approach is suitable for use in an online system monitoring setup for interferometric arrays. We have applied the method to our cosmic-ray data collection, a collection of measurements of short pulses from extensive air showers, recorded by the LOFAR radio telescope. Per air shower, we have collected 2 ms of raw tim...
Time series modeling for syndromic surveillance
Directory of Open Access Journals (Sweden)
Mandl Kenneth D
2003-01-01
Full Text Available Abstract Background Emergency department (ED based syndromic surveillance systems identify abnormally high visit rates that may be an early signal of a bioterrorist attack. For example, an anthrax outbreak might first be detectable as an unusual increase in the number of patients reporting to the ED with respiratory symptoms. Reliably identifying these abnormal visit patterns requires a good understanding of the normal patterns of healthcare usage. Unfortunately, systematic methods for determining the expected number of (ED visits on a particular day have not yet been well established. We present here a generalized methodology for developing models of expected ED visit rates. Methods Using time-series methods, we developed robust models of ED utilization for the purpose of defining expected visit rates. The models were based on nearly a decade of historical data at a major metropolitan academic, tertiary care pediatric emergency department. The historical data were fit using trimmed-mean seasonal models, and additional models were fit with autoregressive integrated moving average (ARIMA residuals to account for recent trends in the data. The detection capabilities of the model were tested with simulated outbreaks. Results Models were built both for overall visits and for respiratory-related visits, classified according to the chief complaint recorded at the beginning of each visit. The mean absolute percentage error of the ARIMA models was 9.37% for overall visits and 27.54% for respiratory visits. A simple detection system based on the ARIMA model of overall visits was able to detect 7-day-long simulated outbreaks of 30 visits per day with 100% sensitivity and 97% specificity. Sensitivity decreased with outbreak size, dropping to 94% for outbreaks of 20 visits per day, and 57% for 10 visits per day, all while maintaining a 97% benchmark specificity. Conclusions Time series methods applied to historical ED utilization data are an important tool
Time series models of symptoms in schizophrenia.
Tschacher, Wolfgang; Kupper, Zeno
2002-12-15
The symptom courses of 84 schizophrenia patients (mean age: 24.4 years; mean previous admissions: 1.3; 64% males) of a community-based acute ward were examined to identify dynamic patterns of symptoms and to investigate the relation between these patterns and treatment outcome. The symptoms were monitored by systematic daily staff ratings using a scale composed of three factors: psychoticity, excitement, and withdrawal. Patients showed moderate to high symptomatic improvement documented by effect size measures. Each of the 84 symptom trajectories was analyzed by time series methods using vector autoregression (VAR) that models the day-to-day interrelations between symptom factors. Multiple and stepwise regression analyses were then performed on the basis of the VAR models. Two VAR parameters were found to be associated significantly with favorable outcome in this exploratory study: 'withdrawal preceding a reduction of psychoticity' as well as 'excitement preceding an increase of withdrawal'. The findings were interpreted as generating hypotheses about how patients cope with psychotic episodes.
Testing whether a time series is Guassian
Energy Technology Data Exchange (ETDEWEB)
Lee, S.
1991-01-01
The authors first tests whether a stationary linear process with mean 0 is Gaussian. For the invertible processes, he considers the empirical process based on the residuals as the basis of a test procedure. By applying the result of Boldin (1983) and Kreiss (1988), he shows that the process behaves asymptotically like the one based on the true errors. For non-invertible processes, on the other hand, Lee uses the empirical process based on data themselves rather than the one based on residuals. Here, the time series is assumed to be a strongly mixing process with a suitable mixing order. Then, the asymptotic behavior of the empirical process in each case is studied under a sequence of contiguous alternatives, and quadratic functionals of the empirical process are employed for AAR([infinity]) processes in order to compare efficiencies between these two procedures. The rest of the thesis is devoted to extending Boldin's results to nonstationary processes such as unstable AR(p) processes and explosive AR(1) processes, analyzing by means of a general stochastic regression model.
Climate Prediction Center (CPC) Global Precipitation Time Series
National Oceanic and Atmospheric Administration, Department of Commerce — The global precipitation time series provides time series charts showing observations of daily precipitation as well as accumulated precipitation compared to normal...
Climate Prediction Center (CPC) Global Temperature Time Series
National Oceanic and Atmospheric Administration, Department of Commerce — The global temperature time series provides time series charts using station based observations of daily temperature. These charts provide information about the...
Spectral Estimation of Non-Gaussian Time Series
Fabián, Z. (Zdeněk)
2010-01-01
Based on the concept of the scalar score of a probability distribution, we introduce a concept of a scalar score of time series and propose to characterize a non-Gaussian time series by spectral density of its scalar score.
Comparative analysis of Debrecen sunspot catalogues
Győri, L.; Ludmány, A.; Baranyi, T.
2017-02-01
Sunspot area data are important for studying solar activity and its long-term variations. At the Debrecen Heliophysical Observatory, we compiled three sunspot catalogues: the Debrecen Photoheliographic Data (DPD), the SDO/HMI Debrecen Data (HMIDD) and the SOHO/MDI Debrecen Data. For comparison, we also compiled an additional sunspot catalogue, the Greenwich Photoheliographic Data, from the digitized Royal Greenwich Observatory images for 1974-76. By comparing these catalogues when they overlap in time, we can investigate how various factors influence the measured area of sunspots, and, in addition, we can derive area cross-calibration factors for these catalogues. The main findings are as follows. Poorer seeing increases the individual corrected spot areas and decreases the number of small spots. Interestingly, the net result of these two effects for the total corrected spot area is zero. DPD daily total corrected sunspot areas are 5 per cent smaller than the HMIDD ones. Revised DPD daily total corrected umbra areas are 9 per cent smaller than those of HMIDD. The Greenwich photoheliographic areas are only a few per cent smaller than DPD areas. A 0.2° difference between the north directions of the DPD and MDI images is found. This value is nearly the same as was found (0.22°) by us in a previous paper comparing HMI and MDI images. The area measurement practice (spots smaller than 10 mh were not directly measured but an area of 2 mh was assigned to each) of the Solar Observing Optical Network cannot explain the large area deficit of the Solar Observing Optical Network.
Coordination failure caused by sunspots
DEFF Research Database (Denmark)
Beugnot, Julie; Gürgüç, Zeynep; Øvlisen, Frederik Roose
2012-01-01
In a coordination game with Pareto-ranked equilibria, we study whether a sunspot can lead to either coordination on an inferior equilibrium (mis-coordination) or to out-of equilibrium behavior (dis-coordination). While much of the literature searches for mechanisms to attain coordination...... on the efficient equilibrium, we consider sunspots as a potential reason for coordination failure. We conduct an experiment with a three player 2x2x2 game in which coordination on the efficient equilibrium is easy and should normally occur. In the control session, we find almost perfect coordination on the payoff......-dominant equilibrium, but in the sunspot treatment, dis-coordination is frequent. Sunspots lead to significant inefficiency, and we conclude that sunspots can indeed cause coordination failure....
An introduction to state space time series analysis.
Commandeur, J.J.F. & Koopman, S.J.
2007-01-01
Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor with state space methods. The only background required in order to understand the material presented in the book is a basic knowledge of classical linear regression models, of which a brief review is...
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui
2014-07-01
The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
Seasonal Time Series Analysis Based on Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Pattern discovery from the seasonal time-series is of importance. Traditionally, most of the algorithms of pattern discovery in time series are similar. A novel mode of time series is proposed which integrates the Genetic Algorithm (GA) for the actual problem. The experiments on the electric power yield sequence models show that this algorithm is practicable and effective.
Theoretical modeling of propagation of magneto-acoustic waves in magnetic regions below sunspots
Khomenko, E; Collados, M; Parchevsky, K; Olshevsky, V
2008-01-01
We use 2D numerical simulations and eikonal approximation to study properties of magneto-acoustic gravity waves traveling below the solar surface through the magnetic structure of sunspots. We consider a series of magnetostatic models of sunspots of different magnetic field strengths, from the deep interior to the chromosphere. The purpose of these studies is to quantify the effect of the magnetic field on local helioseismology measurements. Waves are excited by a sub-photospheric source located in the region beta slightly larger than 1. Time-distance diagrams and travel times are calculated for various frequency intervals and compared to the non-magnetic case. The results confirm that the observed time-distance helioseismology signals in sunspot regions correspond to fast MHD waves. The slow MHD waves form a distinctly different pattern in the time-distance diagram, which has not been detected in observations. The numerical results are in good agreement with the solution in the short-wavelength (eikonal) app...
Sunspot Umbral Oscillations: Results from SOHO JOP097
O'Shea, E.; Muglach, K.; Fleck, B.
2003-10-01
We present results of an ongoing analysis of time series data, which were obtained in the context of the Joint Observing Program (JOP) 97 of the year 2000. This JOP included the Coronal Diagnostic Spectrometer (CDS) and the Michelson Doppler Imager (MDI) instrument, both part of SOHO, the TRACE satellite and various ground based observatories. We show evidence for apparently upwardly propagating in a sunspot umbra which we suggest are due to magnetoacoustic waves. These waves manifest themselves as oscillations in lines ranging in temperature from the upper photosphere/chromosphere to the corona. To our knowledge this is the first time umbral oscillations have been conclusively seen in coronal lines. This research is part of the European Solar Magnetometry Network (ESMN) supported by the EU through the TMR programme.
Generalized Framework for Similarity Measure of Time Series
Directory of Open Access Journals (Sweden)
Hongsheng Yin
2014-01-01
Full Text Available Currently, there is no definitive and uniform description for the similarity of time series, which results in difficulties for relevant research on this topic. In this paper, we propose a generalized framework to measure the similarity of time series. In this generalized framework, whether the time series is univariable or multivariable, and linear transformed or nonlinear transformed, the similarity of time series is uniformly defined using norms of vectors or matrices. The definitions of the similarity of time series in the original space and the transformed space are proved to be equivalent. Furthermore, we also extend the theory on similarity of univariable time series to multivariable time series. We present some experimental results on published time series datasets tested with the proposed similarity measure function of time series. Through the proofs and experiments, it can be claimed that the similarity measure functions of linear multivariable time series based on the norm distance of covariance matrix and nonlinear multivariable time series based on kernel function are reasonable and practical.
Analytical Model of an Asymmetric Sunspot with a Steady Plasma Flow in its Penumbra
Solov'ev, A. A.; Kirichek, E. A.
2016-08-01
A new exact analytical solution to the stationary problem of ideal magnetohydrodynamics is derived for an unipolar asymmetric sunspot immersed in a realistic solar atmosphere. The radial and vertical profiles of pressure, plasma density, and temperature in the visible layers of the sunspot are calculated. The reduction in plasma density in the magnetic funnel of the sunspot, corresponding to the Wilson depression, is also obtained. The magnetic structure of the sunspot is given analytically in a realistic way: a part of the magnetic flux of the sunspot approaches the surrounding photosphere at the outer edge of the penumbra. The magnetic field of the sunspot is not assumed to be axially symmetric. For the first time, the angular dependence of the physical variables in this model allows us to simulate not only a deviation from the circular shape of the sunspot, but also a fine filamentary structure of the sunspot penumbra. The Alfvén Mach number (the ratio of the plasma speed to the Alfvén speed) is zero at the center of the sunspot and rises slowly toward the periphery of the sunspot; this corresponds to the structure of the Evershed flow in the penumbra. The Evershed flow in our model is mainly concentrated in dark penumbral filaments, as is observed.
ANCOVA Procedures in Time-Series Experiments: An Illustrative Example.
Willson, Victor L.
A statistical model for analysis of multiple time-series observation is briefly outlined. The model incorporates a change parameter corresponding to intervention or interruption of the dependent series. The additional time-series are included in the model as covariates. The practical application of the procedure is illustrated with traffic…
Hidden Markov Models for Time Series An Introduction Using R
Zucchini, Walter
2009-01-01
Illustrates the flexibility of HMMs as general-purpose models for time series data. This work presents an overview of HMMs for analyzing time series data, from continuous-valued, circular, and multivariate series to binary data, bounded and unbounded counts and categorical observations.
Time and ensemble averaging in time series analysis
Latka, Miroslaw; Jernajczyk, Wojciech; West, Bruce J
2010-01-01
In many applications expectation values are calculated by partitioning a single experimental time series into an ensemble of data segments of equal length. Such single trajectory ensemble (STE) is a counterpart to a multiple trajectory ensemble (MTE) used whenever independent measurements or realizations of a stochastic process are available. The equivalence of STE and MTE for stationary systems was postulated by Wang and Uhlenbeck in their classic paper on Brownian motion (Rev. Mod. Phys. 17, 323 (1945)) but surprisingly has not yet been proved. Using the stationary and ergodic paradigm of statistical physics -- the Ornstein-Uhlenbeck (OU) Langevin equation, we revisit Wang and Uhlenbeck's postulate. In particular, we find that the variance of the solution of this equation is different for these two ensembles. While the variance calculated using the MTE quantifies the spreading of independent trajectories originating from the same initial point, the variance for STE measures the spreading of two correlated r...
Directory of Open Access Journals (Sweden)
D. M. Willis
2005-03-01
Full Text Available Comprehensive catalogues of ancient sunspot and auroral observations from East Asia are used to identify possible intense historical geomagnetic storms in the interval 210 BC-AD 1918. There are about 270 entries in the sunspot catalogue and about 1150 entries in the auroral catalogue. Special databases have been constructed in which the scientific information in these two catalogues is placed in specified fields. For the purposes of this study, an historical geomagnetic storm is defined in terms of an auroral observation that is apparently associated with a particular sunspot observation, in the sense that the auroral observation occurred within several days of the sunspot observation. More precisely, a selection criterion is formulated for the automatic identification of such geomagnetic storms, using the oriental records stored in the sunspot and auroral databases. The selection criterion is based on specific assumptions about the duration of sunspot visibility with the unaided eye, the likely range of heliographic longitudes of an energetic solar feature, and the likely range of transit times for ejected solar plasma to travel from the Sun to the Earth. This selection criterion results in the identification of nineteen putative historical geomagnetic storms, although two of these storms are spurious in the sense that there are two examples of a single sunspot observation being associated with two different auroral observations separated by more than half a (synodic solar rotation period. The literary and scientific reliabilities of the East Asian sunspot and auroral records that define the nineteen historical geomagnetic storms are discussed in detail in a set of appendices. A possible time sequence of events is presented for each geomagnetic storm, including possible dates for both the central meridian passage of the sunspot and the occurrence of the energetic solar feature, as well as likely transit times for the ejected solar plasma
Scale-dependent intrinsic entropies of complex time series.
Yeh, Jia-Rong; Peng, Chung-Kang; Huang, Norden E
2016-04-13
Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal's complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.
Efficient Algorithms for Segmentation of Item-Set Time Series
Chundi, Parvathi; Rosenkrantz, Daniel J.
We propose a special type of time series, which we call an item-set time series, to facilitate the temporal analysis of software version histories, email logs, stock market data, etc. In an item-set time series, each observed data value is a set of discrete items. We formalize the concept of an item-set time series and present efficient algorithms for segmenting a given item-set time series. Segmentation of a time series partitions the time series into a sequence of segments where each segment is constructed by combining consecutive time points of the time series. Each segment is associated with an item set that is computed from the item sets of the time points in that segment, using a function which we call a measure function. We then define a concept called the segment difference, which measures the difference between the item set of a segment and the item sets of the time points in that segment. The segment difference values are required to construct an optimal segmentation of the time series. We describe novel and efficient algorithms to compute segment difference values for each of the measure functions described in the paper. We outline a dynamic programming based scheme to construct an optimal segmentation of the given item-set time series. We use the item-set time series segmentation techniques to analyze the temporal content of three different data sets—Enron email, stock market data, and a synthetic data set. The experimental results show that an optimal segmentation of item-set time series data captures much more temporal content than a segmentation constructed based on the number of time points in each segment, without examining the item set data at the time points, and can be used to analyze different types of temporal data.
Sparse Representation for Time-Series Classification
2015-02-08
Comput. Vision and Pattern Recognition (CVPR), pp. 4114–4121 (2014). 18. J. Mairal, F. Bach , A. Zisserman, and G. Sapiro. Supervised dictionary learn...ing. In Advances Neural Inform. Process. Syst. (NIPS), pp. 1033–1040 (2008). 19. J. Mairal, F. Bach , and J. Ponce, Task-driven dictionary learning...Series Classification 17 compressive sensing, SISC. 33(1), 250–278 (2011). 41. J. Mairal, F. Bach , J. Ponce, and G. Sapiro, Online dictionary learning for
TIME SERIES ANALYSIS USING A UNIQUE MODEL OF TRANSFORMATION
Directory of Open Access Journals (Sweden)
Goran Klepac
2007-12-01
Full Text Available REFII1 model is an authorial mathematical model for time series data mining. The main purpose of that model is to automate time series analysis, through a unique transformation model of time series. An advantage of this approach of time series analysis is the linkage of different methods for time series analysis, linking traditional data mining tools in time series, and constructing new algorithms for analyzing time series. It is worth mentioning that REFII model is not a closed system, which means that we have a finite set of methods. At first, this is a model for transformation of values of time series, which prepares data used by different sets of methods based on the same model of transformation in a domain of problem space. REFII model gives a new approach in time series analysis based on a unique model of transformation, which is a base for all kind of time series analysis. The advantage of REFII model is its possible application in many different areas such as finance, medicine, voice recognition, face recognition and text mining.
Bernstein polynomials for evolutionary algebraic prediction of short time series
Lukoseviciute, Kristina; Howard, Daniel; Ragulskis, Minvydas
2017-07-01
Short time series prediction technique based on Bernstein polynomials is presented in this paper. Firstly, the straightforward Bernstein polynomial extrapolation scheme is improved by extending the interval of approximation. Secondly, the forecasting scheme is designed in the evolutionary computational setup which is based on the conciliation between the coarseness of the algebraic prediction and the smoothness of the time average prediction. Computational experiments with the test time series suggest that this time series prediction technique could be applicable for various forecasting applications.
Time-series prediction and applications a machine intelligence approach
Konar, Amit
2017-01-01
This book presents machine learning and type-2 fuzzy sets for the prediction of time-series with a particular focus on business forecasting applications. It also proposes new uncertainty management techniques in an economic time-series using type-2 fuzzy sets for prediction of the time-series at a given time point from its preceding value in fluctuating business environments. It employs machine learning to determine repetitively occurring similar structural patterns in the time-series and uses stochastic automaton to predict the most probabilistic structure at a given partition of the time-series. Such predictions help in determining probabilistic moves in a stock index time-series Primarily written for graduate students and researchers in computer science, the book is equally useful for researchers/professionals in business intelligence and stock index prediction. A background of undergraduate level mathematics is presumed, although not mandatory, for most of the sections. Exercises with tips are provided at...
Long Term Sunspot Cycle Phase Coherence with Periodic Phase Disruptions
Pease, Gerald E
2016-01-01
In 1965 Paul D. Jose published his discovery that both the motion of the Sun about the center of mass of the solar system and periods comprised of eight Hale magnetic sunspot cycles with a mean period of ~22.375 years have a matching periodicity of ~179 years. We have investigated the implied link between solar barycentric torque cycles and sunspot cycles and have found that the unsigned solar torque values from 1610 to 2058 are consistently phase and magnitude coherent in ~179 year Jose Cycles. We are able to show that there is also a surprisingly high degree of sunspot cycle phase coherence for times of minima in addition to magnitude correlation of peaks between the nine Schwabe sunspot cycles of 1878 through 1976 (SC12 through SC20) and those of 1699 through 1797 (SC[-5] through SC4). We further identify subsequent subcycles of predominantly non-coherent sunspot cycle phase. In addition we have analyzed the empirical solar motion triggers of both sunspot cycle phase coherence and phase coherence disruptio...
Modeling the Longitudinal Asymmetry in Sunspot Emergence -- the Role of the Wilson Depression
Watson, Fraser; Dalla, Silvia; Marshall, Stephen; 10.1007/s11207-009-9420-z
2009-01-01
The distributions of sunspot longitude at first appearance and at disappearance display an east-west asymmetry that results from a reduction in visibility as one moves from disk centre to the limb. To first order, this is explicable in terms of simple geometrical foreshortening. However, the centre-to-limb visibility variation is much larger than that predicted by foreshortening. Sunspot visibility is also known to be affected by the Wilson effect: the apparent dish shape of the sunspot photosphere caused by the temperature-dependent variation of the geometrical position of the tau=1 layer. In this article we investigate the role of the Wilson effect on the sunspot appearance distributions, deducing a mean depth for the umbral tau=1 layer of 500 to 1500 km. This is based on the comparison of observations of sunspot longitude distribution and Monte Carlo simulations of sunspot appearance using different models for spot growth rate, growth time and depth of Wilson depression.
Modelling the Longitudinal Asymmetry in Sunspot Emergence: The Role of the Wilson Depression
Watson, F.; Fletcher, L.; Dalla, S.; Marshall, S.
2009-11-01
The distributions of sunspot longitude at first appearance and at disappearance display an east-west asymmetry that results from a reduction in visibility as one moves from disk centre to the limb. To first order, this is explicable in terms of simple geometrical foreshortening. However, the centre-to-limb visibility variation is much larger than that predicted by foreshortening. Sunspot visibility is also known to be affected by the Wilson effect: the apparent ‘dish’ shape of the sunspot photosphere caused by the temperature-dependent variation of the geometrical position of the τ=1 layer. In this article we investigate the role of the Wilson effect on the sunspot appearance distributions, deducing a mean depth for the umbral τ=1 layer of 500 - 1500 km. This is based on the comparison of observations of sunspot longitude distribution and Monte Carlo simulations of sunspot appearance using different models for spot growth rate, growth time and depth of Wilson depression.
Ruin Probability in Linear Time Series Model
Institute of Scientific and Technical Information of China (English)
ZHANG Lihong
2005-01-01
This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob's stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both exponential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical results are included to illustrate the accuracy of the non-exponential bound.
Partitioning and interpolation based hybrid ARIMA–ANN model for time series forecasting
Indian Academy of Sciences (India)
C NARENDRA BABU; PALLAVIRAM SURE
2016-07-01
Time series data (TSD) originating from different applications have dissimilar characteristics. Hence for prediction of TSD, diversified varieties of prediction models exist. In many applications, hybrid models provide more accurate predictions than individual models. One such hybrid model, namely auto regressive integrated moving average – artificial neural network (ARIMA–ANN) is devised in many different ways in the literature. However, the prediction accuracy of hybrid ARIMA–ANN model can be further improved by devising suitable processing techniques. In this paper, a hybrid ARIMA–ANN model is proposed, which combines the concepts of the recently developed moving average (MA) filter based hybrid ARIMA–ANN model, with a processing technique involving a partitioning–interpolation (PI) step. The improved prediction accuracy of the proposed PI based hybrid ARIMA–ANN model is justified using a simulation experiment.Further, on different experimental TSD like sunspots TSD and electricity price TSD, the proposed hybrid model is applied along with four existing state-of-the-art models and it is found that the proposed model outperforms all the others, and hence is a promising model for TSD prediction
Analysis of Nonstationary Time Series for Biological Rhythms Research.
Leise, Tanya L
2017-06-01
This article is part of a Journal of Biological Rhythms series exploring analysis and statistics topics relevant to researchers in biological rhythms and sleep research. The goal is to provide an overview of the most common issues that arise in the analysis and interpretation of data in these fields. In this article on time series analysis for biological rhythms, we describe some methods for assessing the rhythmic properties of time series, including tests of whether a time series is indeed rhythmic. Because biological rhythms can exhibit significant fluctuations in their period, phase, and amplitude, their analysis may require methods appropriate for nonstationary time series, such as wavelet transforms, which can measure how these rhythmic parameters change over time. We illustrate these methods using simulated and real time series.
Clustering Time Series Data Stream - A Literature Survey
Kavitha, V
2010-01-01
Mining Time Series data has a tremendous growth of interest in today's world. To provide an indication various implementations are studied and summarized to identify the different problems in existing applications. Clustering time series is a trouble that has applications in an extensive assortment of fields and has recently attracted a large amount of research. Time series data are frequently large and may contain outliers. In addition, time series are a special type of data set where elements have a temporal ordering. Therefore clustering of such data stream is an important issue in the data mining process. Numerous techniques and clustering algorithms have been proposed earlier to assist clustering of time series data streams. The clustering algorithms and its effectiveness on various applications are compared to develop a new method to solve the existing problem. This paper presents a survey on various clustering algorithms available for time series datasets. Moreover, the distinctiveness and restriction ...
On correlations and fractal characteristics of time series
Vitanov, N K; Yankulova, E D; Vitanov, Nikolay K.; Sakai, kenschi; Yankulova, Elka D.
2005-01-01
Correlation analysis is convenient and frequently used tool for investigation of time series from complex systems. Recently new methods such as the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maximum method (WTMM) have been developed. By means of these methods (i) we can investigate long-range correlations in time series and (ii) we can calculate fractal spectra of these time series. But opposite to the classical tool for correlation analysis - the autocorrelation function, the newly developed tools are not applicable to all kinds of time series. The unappropriate application of MFDFA or WTMM leads to wrong results and conclusions. In this article we discuss the opportunities and risks connected to the application of the MFDFA method to time series from a random number generator and to experimentally measured time series (i) for accelerations of an agricultural tractor and (ii) for the heartbeat activity of {\\sl Drosophila melanogaster}. Our main goal is to emphasize ...
A novel weight determination method for time series data aggregation
Xu, Paiheng; Zhang, Rong; Deng, Yong
2017-09-01
Aggregation in time series is of great importance in time series smoothing, predicting and other time series analysis process, which makes it crucial to address the weights in times series correctly and reasonably. In this paper, a novel method to obtain the weights in time series is proposed, in which we adopt induced ordered weighted aggregation (IOWA) operator and visibility graph averaging (VGA) operator and linearly combine the weights separately generated by the two operator. The IOWA operator is introduced to the weight determination of time series, through which the time decay factor is taken into consideration. The VGA operator is able to generate weights with respect to the degree distribution in the visibility graph constructed from the corresponding time series, which reflects the relative importance of vertices in time series. The proposed method is applied to two practical datasets to illustrate its merits. The aggregation of Construction Cost Index (CCI) demonstrates the ability of proposed method to smooth time series, while the aggregation of The Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) illustrate how proposed method maintain the variation tendency of original data.
Non-parametric causal inference for bivariate time series
McCracken, James M
2015-01-01
We introduce new quantities for exploratory causal inference between bivariate time series. The quantities, called penchants and leanings, are computationally straightforward to apply, follow directly from assumptions of probabilistic causality, do not depend on any assumed models for the time series generating process, and do not rely on any embedding procedures; these features may provide a clearer interpretation of the results than those from existing time series causality tools. The penchant and leaning are computed based on a structured method for computing probabilities.
Intrusion Detection Forecasting Using Time Series for Improving Cyber Defence
Abdullah, Azween Bin; Pillai, Thulasyammal Ramiah; Cai, Long Zheng
2015-01-01
The strength of time series modeling is generally not used in almost all current intrusion detection and prevention systems. By having time series models, system administrators will be able to better plan resource allocation and system readiness to defend against malicious activities. In this paper, we address the knowledge gap by investigating the possible inclusion of a statistical based time series modeling that can be seamlessly integrated into existing cyber defense system. Cyber-attack ...
A Generalization of Some Classical Time Series Tools
DEFF Research Database (Denmark)
Nielsen, Henrik Aalborg; Madsen, Henrik
2001-01-01
In classical time series analysis the sample autocorrelation function (SACF) and the sample partial autocorrelation function (SPACF) has gained wide application for structural identification of linear time series models. We suggest generalizations, founded on smoothing techniques, applicable...... for structural identification of non-linear time series models. A similar generalization of the sample cross correlation function is discussed. Furthermore, a measure of the departure from linearity is suggested. It is shown how bootstrapping can be applied to construct confidence intervals under independence...
Genetic programming-based chaotic time series modeling
Institute of Scientific and Technical Information of China (English)
张伟; 吴智铭; 杨根科
2004-01-01
This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust the parameters and takes them as the criteria of established models. Experiments showed the effectiveness of such improvements on chaotic time series modeling.
Information distance and its application in time series
Directory of Open Access Journals (Sweden)
B. Mirza
2008-03-01
Full Text Available In this paper a new method is introduced for studying time series of complex systems. This method is based on using the concept of entropy and Jensen-Shannon divergence. In this paper this method is applied to time series of billiard system and heart signals. By this method, we can diagnose the healthy and unhealthy heart and also chaotic billiards from non chaotic systems . The method can also be applied to other time series.
Predicting Chaotic Time Series Using Recurrent Neural Network
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-Shu; XIAO Xian-Ci
2000-01-01
A new proposed method, i.e. the recurrent neural network (RNN), is introduced to predict chaotic time series. The effectiveness of using RNN for making one-step and multi-step predictions is tested based on remarkable few datum points by computer-generated chaotic time series. Numerical results show that the RNN proposed here is a very powerful tool for making prediction of chaotic time series.
Solar transition region above sunspots
Tian, H; Teriaca, L; Landi, E; Marsch, E
2009-01-01
We study the TR properties above sunspots and the surrounding plage regions, by analyzing several sunspot spectra obtained by SUMER in March 1999 and November 2006. We compare the SUMER spectra observed in the umbra, penumbra, plage, and sunspot plume regions. The Lyman line profiles averaged in each region are presented. For the sunspot observed in 2006, the electron densities, DEM, and filling factors of the TR plasma in the four regions are also investigated. The self-reversals of the Lyman line profiles are almost absent in umbral regions at different locations (heliocentric angle up to $49^\\circ$) on the solar disk. In the sunspot plume, the Lyman lines are also not reversed, whilst the lower Lyman line profiles observed in the plage region are obviously reversed. The TR densities of the umbra and plume are similar and one order of magnitude lower than those of the plage and penumbra. The DEM curve of the sunspot plume exhibits a peak centered around $\\log(T/\\rm{K})\\sim5.45$, which exceeds the DEM of oth...
Trend time-series modeling and forecasting with neural networks.
Qi, Min; Zhang, G Peter
2008-05-01
Despite its great importance, there has been no general consensus on how to model the trends in time-series data. Compared to traditional approaches, neural networks (NNs) have shown some promise in time-series forecasting. This paper investigates how to best model trend time series using NNs. Four different strategies (raw data, raw data with time index, detrending, and differencing) are used to model various trend patterns (linear, nonlinear, deterministic, stochastic, and breaking trend). We find that with NNs differencing often gives meritorious results regardless of the underlying data generating processes (DGPs). This finding is also confirmed by the real gross national product (GNP) series.
gatspy: General tools for Astronomical Time Series in Python
VanderPlas, Jake
2016-10-01
Gatspy contains efficient, well-documented implementations of several common routines for Astronomical time series analysis, including the Lomb-Scargle periodogram, the Supersmoother method, and others.
Using neural networks for dynamic light scattering time series processing
Chicea, Dan
2017-04-01
A basic experiment to record dynamic light scattering (DLS) time series was assembled using basic components. The DLS time series processing using the Lorentzian function fit was considered as reference. A Neural Network was designed and trained using simulated frequency spectra for spherical particles in the range 0–350 nm, assumed to be scattering centers, and the neural network design and training procedure are described in detail. The neural network output accuracy was tested both on simulated and on experimental time series. The match with the DLS results, considered as reference, was good serving as a proof of concept for using neural networks in fast DLS time series processing.
Forecasting the underlying potential governing climatic time series
Livina, V N; Mudelsee, M; Lenton, T M
2012-01-01
We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for `potential analysis' of climatic tipping points which altogether serves anticipating, detecting and forecasting climate transitions and bifurcations using several independent techniques of time series analysis.
Efficient use of correlation entropy for analysing time series data
Indian Academy of Sciences (India)
K P Harikrishnan; R Misra; G Ambika
2009-02-01
The correlation dimension 2 and correlation entropy 2 are both important quantifiers in nonlinear time series analysis. However, use of 2 has been more common compared to 2 as a discriminating measure. One reason for this is that 2 is a static measure and can be easily evaluated from a time series. However, in many cases, especially those involving coloured noise, 2 is regarded as a more useful measure. Here we present an efficient algorithmic scheme to compute 2 directly from a time series data and show that 2 can be used as a more effective measure compared to 2 for analysing practical time series involving coloured noise.
Time series analysis in the social sciences the fundamentals
Shin, Youseop
2017-01-01
Times Series Analysis in the Social Sciences is a practical and highly readable introduction written exclusively for students and researchers whose mathematical background is limited to basic algebra. The book focuses on fundamental elements of time series analysis that social scientists need to understand so they can employ time series analysis for their research and practice. Through step-by-step explanations and using monthly violent crime rates as case studies, this book explains univariate time series from the preliminary visual analysis through the modeling of seasonality, trends, and re
The causality between the rapid rotation of a sunspot and an X3.4 flare
Institute of Scientific and Technical Information of China (English)
Xiao-Li Yan; Zhong-Quan Qu; Cheng-Lin Xu; Zhi-Ke Xue; De-Fang Kong
2009-01-01
Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in ac-tive region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neu-tral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field linestwisting in the photosphere. The twist is then transported into the corona and triggers flares.
Interpretable Early Classification of Multivariate Time Series
Ghalwash, Mohamed F.
2013-01-01
Recent advances in technology have led to an explosion in data collection over time rather than in a single snapshot. For example, microarray technology allows us to measure gene expression levels in different conditions over time. Such temporal data grants the opportunity for data miners to develop algorithms to address domain-related problems,…
Flare differentially rotates sunspot on Sun's surface
Liu, Chang; Xu, Yan; Cao, Wenda; Deng, Na; Lee, Jeongwoo; Hudson, Hugh S.; Gary, Dale E.; Wang, Jiasheng; Jing, Ju; Wang, Haimin
2016-10-01
Sunspots are concentrations of magnetic field visible on the solar surface (photosphere). It was considered implausible that solar flares, as resulted from magnetic reconnection in the tenuous corona, would cause a direct perturbation of the dense photosphere involving bulk motion. Here we report the sudden flare-induced rotation of a sunspot using the unprecedented spatiotemporal resolution of the 1.6 m New Solar Telescope, supplemented by magnetic data from the Solar Dynamics Observatory. It is clearly observed that the rotation is non-uniform over the sunspot: as the flare ribbon sweeps across, its different portions accelerate (up to ~50° h-1) at different times corresponding to peaks of flare hard X-ray emission. The rotation may be driven by the surface Lorentz-force change due to the back reaction of coronal magnetic restructuring and is accompanied by a downward Poynting flux. These results have direct consequences for our understanding of energy and momentum transportation in the flare-related phenomena.
Flare differentially rotates sunspot on Sun's surface
Liu, Chang; Cao, Wenda; Deng, Na; Lee, Jeongwoo; Hudson, Hugh S; Gary, Dale E; Wang, Jiasheng; Jing, Ju; Wang, Haimin
2016-01-01
Sunspots are concentrations of magnetic field visible on the solar surface (photosphere). It was considered implausible that solar flares, as resulted from magnetic reconnection in the tenuous corona, would cause a direct perturbation of the dense photosphere involving bulk motion. Here we report the sudden flare-induced rotation of a sunspot using the unprecedented spatiotemporal resolution of the 1.6 m New Solar Telescope, supplemented by magnetic data from the Solar Dynamics Observatory. It is clearly observed that the rotation is non-uniform over the sunspot: as the flare ribbon sweeps across, its different portions accelerate (up to 50 deg per hr) at different times corresponding to peaks of flare hard X-ray emission. The rotation may be driven by the surface Lorentz-force change due to the back reaction of coronal magnetic restructuring and is accompanied by a downward Poynting flux. These results have direct consequences for our understanding of energy and momentum transportation in the flare-related p...
Flare differentially rotates sunspot on Sun's surface.
Liu, Chang; Xu, Yan; Cao, Wenda; Deng, Na; Lee, Jeongwoo; Hudson, Hugh S; Gary, Dale E; Wang, Jiasheng; Jing, Ju; Wang, Haimin
2016-10-10
Sunspots are concentrations of magnetic field visible on the solar surface (photosphere). It was considered implausible that solar flares, as resulted from magnetic reconnection in the tenuous corona, would cause a direct perturbation of the dense photosphere involving bulk motion. Here we report the sudden flare-induced rotation of a sunspot using the unprecedented spatiotemporal resolution of the 1.6 m New Solar Telescope, supplemented by magnetic data from the Solar Dynamics Observatory. It is clearly observed that the rotation is non-uniform over the sunspot: as the flare ribbon sweeps across, its different portions accelerate (up to ∼50° h(-1)) at different times corresponding to peaks of flare hard X-ray emission. The rotation may be driven by the surface Lorentz-force change due to the back reaction of coronal magnetic restructuring and is accompanied by a downward Poynting flux. These results have direct consequences for our understanding of energy and momentum transportation in the flare-related phenomena.
Studies on time series applications in environmental sciences
Bărbulescu, Alina
2016-01-01
Time series analysis and modelling represent a large study field, implying the approach from the perspective of the time and frequency, with applications in different domains. Modelling hydro-meteorological time series is difficult due to the characteristics of these series, as long range dependence, spatial dependence, the correlation with other series. Continuous spatial data plays an important role in planning, risk assessment and decision making in environmental management. In this context, in this book we present various statistical tests and modelling techniques used for time series analysis, as well as applications to hydro-meteorological series from Dobrogea, a region situated in the south-eastern part of Romania, less studied till now. Part of the results are accompanied by their R code. .
Simulation of Ground Winds Time Series
Adelfang, S. I.
2008-01-01
A simulation process has been developed for generation of the longitudinal and lateral components of ground wind atmospheric turbulence as a function of mean wind speed, elevation, temporal frequency range and distance between locations. The distance between locations influences the spectral coherence between the simulated series at adjacent locations. Short distances reduce correlation only at high frequencies; as distances increase correlation is reduced over a wider range of frequencies. The choice of values for the constants d1 and d3 in the PSD model is the subject of work in progress. An improved knowledge of the values for zO as a function of wind direction at the ARES-1 launch pads is necessary for definition of d1. Results of other studies at other locations may be helpful as summarized in Fichtl's recent correspondence. Ideally, further research is needed based on measurements of ground wind turbulence with high resolution anemometers at a number of altitudes at a new KSC tower located closer to the ARES-1 launch pad .The proposed research would be based on turbulence measurements that may be influenced by surface terrain roughness that may be significantly different from roughness prior to 1970 in Fichtl's measurements. Significant improvements in instrumentation, data storage end processing will greatly enhance the capability to model ground wind profiles and ground wind turbulence.
How to analyse irregularly sampled geophysical time series?
Eroglu, Deniz; Ozken, Ibrahim; Stemler, Thomas; Marwan, Norbert; Wyrwoll, Karl-Heinz; Kurths, Juergen
2015-04-01
One of the challenges of time series analysis is to detect dynamical changes in the dynamics of the underlying system.There are numerous methods that can be used to detect such regime changes in regular sampled times series. Here we present a new approach, that can be applied, when the time series is irregular sampled. Such data sets occur frequently in real world applications as in paleo climate proxy records. The basic idea follows Victor and Purpura [1] and considers segments of the time series. For each segment we compute the cost of transforming the segment into the following one. If the time series is from one dynamical regime the cost of transformation should be similar for each segment of the data. Dramatic changes in the cost time series indicate a change in the underlying dynamics. Any kind of analysis can be applicable to the cost time series since it is a regularly sampled time series. While recurrence plots are not the best choice for irregular sampled data with some measurement noise component, we show that a recurrence plot analysis based on the cost time series can successfully identify the changes in the dynamics of the system. We tested this method using synthetically created time series and will use these results to highlight the performance of our method. Furthermore we present our analysis of a suite of calcite and aragonite stalagmites located in the eastern Kimberley region of tropical Western Australia. This oxygen isotopic data is a proxy for the monsoon activity over the last 8,000 years. In this time series our method picks up several so far undetected changes from wet to dry in the monsoon system and therefore enables us to get a better understanding of the monsoon dynamics in the North-East of Australia over the last couple of thousand years. [1] J. D. Victor and K. P. Purpura, Network: Computation in Neural Systems 8, 127 (1997)
A Method for Determining Periods in Time Series.
1981-04-01
SUPPLEMENTARY NOTES IS. KEY WORDS (Conlinu an revere cide Ii necesry d Identify by block nmi 9ber) Univariate time series; spectral density function ; Newton’s...and the method is applied to a series of hormone levels data. KEY WORDS: Univariate time series; Spectral density function ; Newton’s Method...Z the set of integers, be a zero mean covariance stationary time series with autocovariance function R(v) = E(Y(t)Y(t+v)), vZ and spectral density function f
Distance measure with improved lower bound for multivariate time series
Li, Hailin
2017-02-01
Lower bound function is one of the important techniques used to fast search and index time series data. Multivariate time series has two aspects of high dimensionality including the time-based dimension and the variable-based dimension. Due to the influence of variable-based dimension, a novel method is proposed to deal with the lower bound distance computation for multivariate time series. The proposed method like the traditional ones also reduces the dimensionality of time series in its first step and thus does not directly apply the lower bound function on the multivariate time series. The dimensionality reduction is that multivariate time series is reduced to univariate time series denoted as center sequences according to the principle of piecewise aggregate approximation. In addition, an extended lower bound function is designed to obtain good tightness and fast measure the distance between any two center sequences. The experimental results demonstrate that the proposed lower bound function has better tightness and improves the performance of similarity search in multivariate time series datasets.
Recovery of the Time-Evolution Equation of Time-Delay Systems from Time Series
Bünner, M J; Kittel, A; Parisi, J; Meyer, Th.
1997-01-01
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a second step, the time-delay differential equation can be recovered from the time series. The method is a generalization of our recently proposed method suitable for time series analysis of {\\it scalar} time-delay systems. The dynamics is not required to be settled on its attractor, which also makes transient motion accessible to the analysis. If the motion actually takes place on a chaotic attractor, the applicability of the method does not depend on the dimensionality of the chaotic attractor - one main advantage over all time series analysis methods known until now. For demonstration, we analyze time series, which are obtained with the help of the numerical integration of a two-dimensional time-delay differential equation. After having determined the delay time, we recover...
Multiscale structure of time series revealed by the monotony spectrum.
Vamoş, Călin
2017-03-01
Observation of complex systems produces time series with specific dynamics at different time scales. The majority of the existing numerical methods for multiscale analysis first decompose the time series into several simpler components and the multiscale structure is given by the properties of their components. We present a numerical method which describes the multiscale structure of arbitrary time series without decomposing them. It is based on the monotony spectrum defined as the variation of the mean amplitude of the monotonic segments with respect to the mean local time scale during successive averagings of the time series, the local time scales being the durations of the monotonic segments. The maxima of the monotony spectrum indicate the time scales which dominate the variations of the time series. We show that the monotony spectrum can correctly analyze a diversity of artificial time series and can discriminate the existence of deterministic variations at large time scales from the random fluctuations. As an application we analyze the multifractal structure of some hydrological time series.
Time series prediction using wavelet process neural network
Institute of Scientific and Technical Information of China (English)
Ding Gang; Zhong Shi-Sheng; Li Yang
2008-01-01
In the real world, the inputs of many complicated systems are time-varying functions or processes. In order to predict the outputs of these systems with high speed and accuracy, this paper proposes a time series prediction model based on the wavelet process neural network, and develops the corresponding learning algorithm based on the expansion of the orthogonal basis functions. The effectiveness of the proposed time series prediction model and its learning algorithm is proved by the Mackey-Glass time series prediction, and the comparative prediction results indicate that the proposed time series prediction model based on the wavelet process neural network seems to perform well and appears suitable for using as a good tool to predict the highly complex nonlinear time series.
Small Sample Properties of Bayesian Multivariate Autoregressive Time Series Models
Price, Larry R.
2012-01-01
The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying…
Measurements of spatial population synchrony: influence of time series transformations.
Chevalier, Mathieu; Laffaille, Pascal; Ferdy, Jean-Baptiste; Grenouillet, Gaël
2015-09-01
Two mechanisms have been proposed to explain spatial population synchrony: dispersal among populations, and the spatial correlation of density-independent factors (the "Moran effect"). To identify which of these two mechanisms is driving spatial population synchrony, time series transformations (TSTs) of abundance data have been used to remove the signature of one mechanism, and highlight the effect of the other. However, several issues with TSTs remain, and to date no consensus has emerged about how population time series should be handled in synchrony studies. Here, by using 3131 time series involving 34 fish species found in French rivers, we computed several metrics commonly used in synchrony studies to determine whether a large-scale climatic factor (temperature) influenced fish population dynamics at the regional scale, and to test the effect of three commonly used TSTs (detrending, prewhitening and a combination of both) on these metrics. We also tested whether the influence of TSTs on time series and population synchrony levels was related to the features of the time series using both empirical and simulated time series. For several species, and regardless of the TST used, we evidenced a Moran effect on freshwater fish populations. However, these results were globally biased downward by TSTs which reduced our ability to detect significant signals. Depending on the species and the features of the time series, we found that TSTs could lead to contradictory results, regardless of the metric considered. Finally, we suggest guidelines on how population time series should be processed in synchrony studies.
Transition Icons for Time Series Visualization and Exploratory Analysis.
Nickerson, Paul; Baharloo, Raheleh; Wanigatunga, Amal A; Manini, Todd D; Tighe, Patrick J; Rashidi, Parisa
2017-05-16
The modern healthcare landscape has seen the rapid emergence of techniques and devices which temporally monitor and record physiological signals. The prevalence of time series data within the healthcare field necessitates the development of methods which can analyze the data in order to draw meaningful conclusions. Time series behavior is notoriously difficult to intuitively understand due to its intrinsic high-dimensionality, which is compounded in the case of analyzing groups of time series collected from different patients. Our framework, which we call Transition Icons, renders common patterns in a visual format useful for understanding the shared behavior within groups of time series. Transition Icons are adept at detecting and displaying subtle differences and similarities e.g. between measurements taken from patients receiving different treatment strategies or stratified by demographics. We introduce various methods which collectively allow for exploratory analysis of groups of time series, while being free of distribution assumptions and including simple heuristics for parameter determination. Our technique extracts discrete transition patterns from Symbolic Aggregate approXimation (SAX) representations, and compiles transition frequencies into a Bag of Patterns (BoP) constructed for each group. These transition frequencies are normalized and aligned in icon form to intuitively display the underlying patterns. We demonstrate the Transition Icon technique for two time series data sets - postoperative pain scores, and hip-worn accelerometer activity counts. We believe Transition Icons can be an important tool for researchers approaching time series data, as they give rich and intuitive information about collective time series behaviors.
Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series
DEFF Research Database (Denmark)
Gao, Jiti; Kanaya, Shin; Li, Degui
2015-01-01
This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our...... results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series....
Model of a synthetic wind speed time series generator
DEFF Research Database (Denmark)
Negra, N.B.; Holmstrøm, O.; Bak-Jensen, B.
2008-01-01
of possible wind conditions. If these information are not available, synthetic wind speed time series may be a useful tool as well, but their generator must preserve statistical and stochastic features of the phenomenon. This paper deals with this issue: a generator for synthetic wind speed time series...
Evaluation Applications of Regression Analysis with Time-Series Data.
Veney, James E.
1993-01-01
The application of time series analysis is described, focusing on the use of regression analysis for analyzing time series in a way that may make it more readily available to an evaluation practice audience. Practical guidelines are suggested for decision makers in government, health, and social welfare agencies. (SLD)
Metagenomics meets time series analysis: unraveling microbial community dynamics
Faust, K.; Lahti, L.M.; Gonze, D.; Vos, de W.M.; Raes, J.
2015-01-01
The recent increase in the number of microbial time series studies offers new insights into the stability and dynamics of microbial communities, from the world's oceans to human microbiota. Dedicated time series analysis tools allow taking full advantage of these data. Such tools can reveal periodic
Two-fractal overlap time series: Earthquakes and market crashes
Indian Academy of Sciences (India)
Bikas K Chakrabarti; Arnab Chatterjee; Pratip Bhattacharyya
2008-08-01
We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.
Robust Forecasting of Non-Stationary Time Series
Croux, C.; Fried, R.; Gijbels, I.; Mahieu, K.
2010-01-01
This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable foreca
Mean shifts, unit roots and forecasting seasonal time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard); H. Hoek (Henk)
1997-01-01
textabstractExamples of descriptive models for changing seasonal patterns in economic time series are autoregressive models with seasonal unit roots or with deterministic seasonal mean shifts. In this paper we show through a forecasting comparison for three macroeconomic time series (for which tests
Stata: The language of choice for time series analysis?
Baum, Christopher F
2004-01-01
This paper discusses the use of Stata for the analysis of time series and panel data. The evolution of time-series capabilities in Stata is reviewed. Facilities for data management, graphics, and econometric analysis from both official Stata and the user community are discussed. A new routine to provide moving-window regression estimates, rollreg, is described, and its use illustrated.
Fixed Points in Self-Similar Analysis of Time Series
Gluzman, S.; Yukalov, V. I.
1998-01-01
Two possible definitions of fixed points in the self-similar analysis of time series are considered. One definition is based on the minimal-difference condition and another, on a simple averaging. From studying stock market time series, one may conclude that these two definitions are practically equivalent. A forecast is made for the stock market indices for the end of March 1998.
Parameterizing unconditional skewness in models for financial time series
DEFF Research Database (Denmark)
He, Changli; Silvennoinen, Annastiina; Teräsvirta, Timo
In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate...
Time Series Econometrics for the 21st Century
Hansen, Bruce E.
2017-01-01
The field of econometrics largely started with time series analysis because many early datasets were time-series macroeconomic data. As the field developed, more cross-sectional and longitudinal datasets were collected, which today dominate the majority of academic empirical research. In nonacademic (private sector, central bank, and governmental)…
Mean shifts, unit roots and forecasting seasonal time series
Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard); H. Hoek (Henk)
1997-01-01
textabstractExamples of descriptive models for changing seasonal patterns in economic time series are autoregressive models with seasonal unit roots or with deterministic seasonal mean shifts. In this paper we show through a forecasting comparison for three macroeconomic time series (for which tests
Time series analysis : Smoothed correlation integrals, autocovariances, and power spectra
Takens, F; Dumortier, F; Broer, H; Mawhin, J; Vanderbauwhede, A; Lunel, SV
2005-01-01
In this paper we relate notions from linear time series analyses, like autocovariances and power spectra, with notions from nonlinear times series analysis, like (smoothed) correlation integrals and the corresponding dimensions and entropies. The complete proofs of the results announced in this pape
Choudhary, Debi Prasad
2010-01-01
We used the flux calibrated images through the Broad Band Filter Imager and Stokes Polarimeter data obtained with the Solar Optical Telescope onboard the Hinode spacecraft to study the properties of bright points in and around the sunspots. The well isolated bright points were selected and classified as umbral dot, peripheral umbral dot, penumbral grains and G-band bright point depending on their location. Most of the bright points are smaller than about 150 km. The larger points are mostly associated with the penumbral features. The bright points are not uniformly distributed over the umbra but preferentially located around the penumbral boundary and in the fast decaying parts of umbra. The color temperature of the bright points, derived using the continuum irradiance, are in the range of 4600 K to 6600 K with cooler ones located in the umbra. The temperature increases as a function of distance from the center to outside. The G-band, CN-band and CaII H flux of the bright points as a function of their blue ba...
Transition of the Sunspot Number from Zurich to Brussels in 1980: A Personal Perspective
Stenflo, J. O.
2016-11-01
The Swiss Federal Observatory, which had been founded in 1863 by Rudolf Wolf, was dissolved in connection with the retirement of Max Waldmeier in 1979. The determination of the Zurich sunpot number, which had been a cornerstone activity of the observatory, was then discontinued by ETH Zurich. A smooth transition of the responsibility for the sunspot number from Zurich to Brussels was achieved in 1980, however, through which it was possible to avoid a discontinuity in this important time series. Here we describe the circumstances that led to the termination in Zurich, how Brussels was chosen for the succession, and how the transfer was accomplished.
The Effect of Sunspot Weighting
Svalgaard, Leif; Cagnotti, Marco; Cortesi, Sergio
2017-02-01
Although W. Brunner began to weight sunspot counts (from 1926), using a method whereby larger spots were counted more than once, he compensated for the weighting by not counting enough smaller spots in order to maintain the same reduction factor (0.6) as was used by his predecessor A. Wolfer to reduce the count to R. Wolf's original scale, so that the weighting did not have any effect on the scale of the sunspot number. In 1947, M. Waldmeier formalized the weighting (on a scale from 1 to 5) of the sunspot count made at Zurich and its auxiliary station Locarno. This explicit counting method, when followed, inflates the relative sunspot number over that which corresponds to the scale set by Wolfer (and matched by Brunner). Recounting some 60,000 sunspots on drawings from the reference station Locarno shows that the number of sunspots reported was "over counted" by {≈} 44 % on average, leading to an inflation (measured by an effective weight factor) in excess of 1.2 for high solar activity. In a double-blind parallel counting by the Locarno observer M. Cagnotti, we determined that Svalgaard's count closely matches that of Cagnotti, allowing us to determine from direct observation the daily weight factor for spots since 2003 (and sporadically before). The effective total inflation turns out to have two sources: a major one (15 - 18 %) caused by weighting of spots, and a minor source (4 - 5 %) caused by the introduction of the Zürich classification of sunspot groups which increases the group count by 7 - 8 % and the relative sunspot number by about half that. We find that a simple empirical equation (depending on the activity level) fits the observed factors well, and use that fit to estimate the weighting inflation factor for each month back to the introduction of effective inflation in 1947 and thus to be able to correct for the over-counts and to reduce sunspot counting to the Wolfer method in use from 1894 onwards.
Scale Invariance in Rain Time Series
Deluca, A.; Corral, A.
2009-09-01
In the last few years there have been pieces of evidence that rain events can be considered analogous to other nonequilibrium relaxation processes in Nature such as earthquakes, solar flares and avalanches. In this work we compare the probability densities of rain event size, duration, and recurrence times (i.e., drought periods) between one Mediterranean site and different sites worldwide. We test the existence of scale invariance in these distributions and the possibility of a universal scaling exponent, despite the different climatic characteristics of the different places.
A Standard Law for the Equatorward Drift of the Sunspot Zones
Hathaway, David H.
2012-01-01
The latitudinal location of the sunspot zones in each hemisphere is determined by calculating the centroid position of sunspot areas for each solar rotation from May 1874 to June 2012. When these centroid positions are plotted and analyzed as functions of time from each sunspot cycle maximum there appears to be systematic differences in the positions and equatorward drift rates as a function of sunspot cycle amplitude. If, instead, these centroid positions are plotted and analyzed as functions of time from each sunspot cycle minimum then most of the differences in the positions and equatorward drift rates disappear. The differences that remain disappear entirely if curve fitting is used to determine the starting times (which vary by as much as 8 months from the times of minima). The sunspot zone latitudes and equatorward drift measured relative to this starting time follow a standard path for all cycles with no dependence upon cycle strength or hemispheric dominance. Although Cycle 23 was peculiar in its length and the strength of the polar fields it produced, it too shows no significant variation from this standard. This standard law, and the lack of variation with sunspot cycle characteristics, is consistent with Dynamo Wave mechanisms but not consistent with current Flux Transport Dynamo models for the equatorward drift of the sunspot zones.
Testing time series reversibility using complex network methods
Donges, Jonathan F; Kurths, Jürgen
2012-01-01
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a set of novel statistical tests for time series reversibility based on standard and horizontal visibility graphs. Specifically, we statistically compare the distributions of time-directed variants of the common graph-theoretical measures degree and local clustering coefficient. Unlike other tests for reversibility, our approach does not require constructing surrogate data and can be applied to relatively short time series. We demonstrate its performance for realisations of paradigmatic model systems with known time-reversal properties as well as pickling up signatures of nonlinearity in some well-studied real-world neuro-physiological time series.
Correlation Between Sunspot Number and ca II K Emission Index
Bertello, Luca; Tlatov, Andrey; Singh, Jagdev
2016-01-01
Long-term synoptic observations in the resonance line of Ca II K constitute a fundamental database for a variety of retrospective analyses of the state of the solar magnetism. Synoptic Ca II K observations began in late 1904 at the Kodaikanal Observatory, in India. In early 1970s, the National Solar Observatory (NSO) at Sacramento Peak (USA) started a new program of daily Sun-as-a-star observations in the Ca II K line. Today the NSO is continuing these observations through its Synoptic Optical Long-term Investigations of the Sun (SOLIS) facility. These different data sets can be combined into a single disk-integrated Ca II K index time series that describes the average properties of the chromospheric emission over several solar cycles. We present such a Ca II K composite and discuss its correlation with the new entirely revised sunspot number data series. For this preliminary investigation, the scaling factor between pairs of time series was determined assuming a simple linear model for the relationship betwe...
Correlation Between Sunspot Number and Ca ii K Emission Index
Bertello, Luca; Pevtsov, Alexei; Tlatov, Andrey; Singh, Jagdev
2016-11-01
Long-term synoptic observations in the resonance line of Ca ii K constitute a fundamental database for a variety of retrospective analyses of the state of the solar magnetism. Synoptic Ca ii K observations began in late 1904 at the Kodaikanal Observatory in India. In the early 1970s, the National Solar Observatory (NSO) at Sacramento Peak (USA) started a new program of daily Sun-as-a-star observations in the Ca ii K line. Today the NSO is continuing these observations through its Synoptic Optical Long-term Investigations of the Sun (SOLIS) facility. These different data sets can be combined into a single disk-integrated Ca ii K index time series that describes the average properties of the chromospheric emission over several solar cycles. We present such a Ca ii K composite and discuss its correlation with the new entirely revised sunspot number data series. For this preliminary investigation, the scaling factor between pairs of time series was determined assuming a simple linear model for the relationship between the monthly mean values during the duration of overlapping observations.
Fisher Information Framework for Time Series Modeling
Venkatesan, R C
2016-01-01
A robust prediction model invoking the Takens embedding theorem, whose \\textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz, central to the \\textit{working hypothesis} satisfy a time independent Schr\\"{o}dinger-like equation in a vector setting. The inference of i) the probability density function of the coefficients of the \\textit{working hypothesis} and ii) the establishing of constraint driven pseudo-inverse condition for the modeling phase of the prediction scheme, is made, for the case of normal distributions, with the aid of the quantum mechanical virial theorem. The well-known reciprocity relations and the associated Legendre transform structure for the Fisher information measure (FIM, hereafter)-based model in a vector setting (with least square constraints) are self-consistently derived. These relations are demonstrated to yield an intriguing form of the FIM for the modeling phase, which defi...
Time series analysis and inverse theory for geophysicists
Institute of Scientific and Technical Information of China (English)
Junzo Kasahara
2006-01-01
@@ Thanks to the advances in geophysical measurement technologies, most geophysical data are now recorded in digital form. But to extract the ‘Earth's nature’ from observed data, it is necessary to apply the signal-processing method to the time-series data, seismograms and geomagnetic records being the most common. The processing of time-series data is one of the major subjects of this book.By the processing of time series data, numerical values such as travel-times are obtained.The first stage of data analysis is forward modeling, but the more advanced step is the inversion method. This is the second subject of this book.
Sensor-Generated Time Series Events: A Definition Language
Anguera, Aurea; Lara, Juan A.; Lizcano, David; Martínez, Maria Aurora; Pazos, Juan
2012-01-01
There are now a great many domains where information is recorded by sensors over a limited time period or on a permanent basis. This data flow leads to sequences of data known as time series. In many domains, like seismography or medicine, time series analysis focuses on particular regions of interest, known as events, whereas the remainder of the time series contains hardly any useful information. In these domains, there is a need for mechanisms to identify and locate such events. In this paper, we propose an events definition language that is general enough to be used to easily and naturally define events in time series recorded by sensors in any domain. The proposed language has been applied to the definition of time series events generated within the branch of medicine dealing with balance-related functions in human beings. A device, called posturograph, is used to study balance-related functions. The platform has four sensors that record the pressure intensity being exerted on the platform, generating four interrelated time series. As opposed to the existing ad hoc proposals, the results confirm that the proposed language is valid, that is generally applicable and accurate, for identifying the events contained in the time series.
Performance of multifractal detrended fluctuation analysis on short time series
Lopez, Juan Luis
2013-01-01
The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series. As an application the series of the daily exchange rate between the U.S. dollar and the euro is studied.
Time Series Decomposition into Oscillation Components and Phase Estimation.
Matsuda, Takeru; Komaki, Fumiyasu
2017-02-01
Many time series are naturally considered as a superposition of several oscillation components. For example, electroencephalogram (EEG) time series include oscillation components such as alpha, beta, and gamma. We propose a method for decomposing time series into such oscillation components using state-space models. Based on the concept of random frequency modulation, gaussian linear state-space models for oscillation components are developed. In this model, the frequency of an oscillator fluctuates by noise. Time series decomposition is accomplished by this model like the Bayesian seasonal adjustment method. Since the model parameters are estimated from data by the empirical Bayes' method, the amplitudes and the frequencies of oscillation components are determined in a data-driven manner. Also, the appropriate number of oscillation components is determined with the Akaike information criterion (AIC). In this way, the proposed method provides a natural decomposition of the given time series into oscillation components. In neuroscience, the phase of neural time series plays an important role in neural information processing. The proposed method can be used to estimate the phase of each oscillation component and has several advantages over a conventional method based on the Hilbert transform. Thus, the proposed method enables an investigation of the phase dynamics of time series. Numerical results show that the proposed method succeeds in extracting intermittent oscillations like ripples and detecting the phase reset phenomena. We apply the proposed method to real data from various fields such as astronomy, ecology, tidology, and neuroscience.
Outliers detection in multivariate time series by independent component analysis.
Baragona, Roberto; Battaglia, Francesco
2007-07-01
In multivariate time series, outlying data may be often observed that do not fit the common pattern. Occurrences of outliers are unpredictable events that may severely distort the analysis of the multivariate time series. For instance, model building, seasonality assessment, and forecasting may be seriously affected by undetected outliers. The structure dependence of the multivariate time series gives rise to the well-known smearing and masking phenomena that prevent using most outliers' identification techniques. It may be noticed, however, that a convenient way for representing multiple outliers consists of superimposing a deterministic disturbance to a gaussian multivariate time series. Then outliers may be modeled as nongaussian time series components. Independent component analysis is a recently developed tool that is likely to be able to extract possible outlier patterns. In practice, independent component analysis may be used to analyze multivariate observable time series and separate regular and outlying unobservable components. In the factor models framework too, it is shown that independent component analysis is a useful tool for detection of outliers in multivariate time series. Some algorithms that perform independent component analysis are compared. It has been found that all algorithms are effective in detecting various types of outliers, such as patches, level shifts, and isolated outliers, even at the beginning or the end of the stretch of observations. Also, there is no appreciable difference in the ability of different algorithms to display the outlying observations pattern.
Solving Nonlinear Time Delay Control Systems by Fourier series
Directory of Open Access Journals (Sweden)
Mohammad Hadi Farahi
2014-06-01
Full Text Available In this paper we present a method to find the solution of time-delay optimal control systems using Fourier series. The method is based upon expanding various time functions in the system as their truncated Fourier series. Operational matrices of integration and delay are presented and are utilized to reduce the solution of time-delay control systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Cross recurrence plot based synchronization of time series
N. Marwan; Thiel, M.; Nowaczyk, N. R.
2002-01-01
The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so ...
Indirect comparison of Debrecen and Greenwich daily sums of sunspot areas
Baranyi, T; Coffey, H E
2013-01-01
Sunspot area data play an important role in the studies of solar activity and its long-term variations. In order to reveal real long-term solar variations precise homogeneous sunspot area databases should be used. However, the measured areas may be burdened with systematic deviations, which may vary in time. Thus, there is a need to investigate the long-term variation of sunspot area datasets and to determine the time-dependent cross-calibration factors. In this study, we investigate the time-dependent differences between the available long-term sunspot databases. Using the results, we estimate the correction factor to calibrate the corrected daily sunspot areas of Debrecen Photoheliographic Data (DPD) to the same data of Greenwich Photoheliographic Results (GPR) by using the overlapping Kislovodsk and Pulkovo data. We give the correction factor as GPR=1.08(\\pm 0.11)*DPD
Clinical time series prediction: Toward a hierarchical dynamical system framework.
Liu, Zitao; Hauskrecht, Milos
2015-09-01
Developing machine learning and data mining algorithms for building temporal models of clinical time series is important for understanding of the patient condition, the dynamics of a disease, effect of various patient management interventions and clinical decision making. In this work, we propose and develop a novel hierarchical framework for modeling clinical time series data of varied length and with irregularly sampled observations. Our hierarchical dynamical system framework for modeling clinical time series combines advantages of the two temporal modeling approaches: the linear dynamical system and the Gaussian process. We model the irregularly sampled clinical time series by using multiple Gaussian process sequences in the lower level of our hierarchical framework and capture the transitions between Gaussian processes by utilizing the linear dynamical system. The experiments are conducted on the complete blood count (CBC) panel data of 1000 post-surgical cardiac patients during their hospitalization. Our framework is evaluated and compared to multiple baseline approaches in terms of the mean absolute prediction error and the absolute percentage error. We tested our framework by first learning the time series model from data for the patients in the training set, and then using it to predict future time series values for the patients in the test set. We show that our model outperforms multiple existing models in terms of its predictive accuracy. Our method achieved a 3.13% average prediction accuracy improvement on ten CBC lab time series when it was compared against the best performing baseline. A 5.25% average accuracy improvement was observed when only short-term predictions were considered. A new hierarchical dynamical system framework that lets us model irregularly sampled time series data is a promising new direction for modeling clinical time series and for improving their predictive performance. Copyright © 2014 Elsevier B.V. All rights reserved.
Clinical time series prediction: towards a hierarchical dynamical system framework
Liu, Zitao; Hauskrecht, Milos
2014-01-01
Objective Developing machine learning and data mining algorithms for building temporal models of clinical time series is important for understanding of the patient condition, the dynamics of a disease, effect of various patient management interventions and clinical decision making. In this work, we propose and develop a novel hierarchical framework for modeling clinical time series data of varied length and with irregularly sampled observations. Materials and methods Our hierarchical dynamical system framework for modeling clinical time series combines advantages of the two temporal modeling approaches: the linear dynamical system and the Gaussian process. We model the irregularly sampled clinical time series by using multiple Gaussian process sequences in the lower level of our hierarchical framework and capture the transitions between Gaussian processes by utilizing the linear dynamical system. The experiments are conducted on the complete blood count (CBC) panel data of 1000 post-surgical cardiac patients during their hospitalization. Our framework is evaluated and compared to multiple baseline approaches in terms of the mean absolute prediction error and the absolute percentage error. Results We tested our framework by first learning the time series model from data for the patient in the training set, and then applying the model in order to predict future time series values on the patients in the test set. We show that our model outperforms multiple existing models in terms of its predictive accuracy. Our method achieved a 3.13% average prediction accuracy improvement on ten CBC lab time series when it was compared against the best performing baseline. A 5.25% average accuracy improvement was observed when only short-term predictions were considered. Conclusion A new hierarchical dynamical system framework that lets us model irregularly sampled time series data is a promising new direction for modeling clinical time series and for improving their predictive
Modeling Persistence In Hydrological Time Series Using Fractional Differencing
Hosking, J. R. M.
1984-12-01
The class of autoregressive integrated moving average (ARIMA) time series models may be generalized by permitting the degree of differencing d to take fractional values. Models including fractional differencing are capable of representing persistent series (d > 0) or short-memory series (d = 0). The class of fractionally differenced ARIMA processes provides a more flexible way than has hitherto been available of simultaneously modeling the long-term and short-term behavior of a time series. In this paper some fundamental properties of fractionally differenced ARIMA processes are presented. Methods of simulating these processes are described. Estimation of the parameters of fractionally differenced ARIMA models is discussed, and an approximate maximum likelihood method is proposed. The methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures.
Seasonality, nonstationarity and the forecasting of monthly time series
Ph.H.B.F. Franses (Philip Hans)
1991-01-01
textabstractWe focus on two forecasting models for a monthly time series. The first model requires that the variable is first order and seasonally differenced. The second model considers the series only in its first differences, while seasonality is modeled with a constant and seasonal dummies. A me
Seasonality, nonstationarity and the forecasting of monthly time series
Ph.H.B.F. Franses (Philip Hans)
1991-01-01
textabstractWe focus on two forecasting models for a monthly time series. The first model requires that the variable is first order and seasonally differenced. The second model considers the series only in its first differences, while seasonality is modeled with a constant and seasonal dummies. A me
A vector of quarters representation for bivariate time series
Ph.H.B.F. Franses (Philip Hans)
1995-01-01
textabstractIn this paper it is shown that several models for a bivariate nonstationary quarterly time series are nested in a vector autoregression with cointegration restrictions for the eight annual series of quarterly observations. Or, the Granger Representation Theorem is extended to incorporate
A multivariate approach to modeling univariate seasonal time series
Ph.H.B.F. Franses (Philip Hans)
1994-01-01
textabstractA seasonal time series can be represented by a vector autoregressive model for the annual series containing the seasonal observations. This model allows for periodically varying coefficients. When the vector elements are integrated, the maximum likelihood cointegration method can be used
Seasonality, nonstationarity and the forecasting of monthly time series
Ph.H.B.F. Franses (Philip Hans)
1991-01-01
textabstractWe focus on two forecasting models for a monthly time series. The first model requires that the variable is first order and seasonally differenced. The second model considers the series only in its first differences, while seasonality is modeled with a constant and seasonal dummies. A
Multivariate time series analysis with R and financial applications
Tsay, Ruey S
2013-01-01
Since the publication of his first book, Analysis of Financial Time Series, Ruey Tsay has become one of the most influential and prominent experts on the topic of time series. Different from the traditional and oftentimes complex approach to multivariate (MV) time series, this sequel book emphasizes structural specification, which results in simplified parsimonious VARMA modeling and, hence, eases comprehension. Through a fundamental balance between theory and applications, the book supplies readers with an accessible approach to financial econometric models and their applications to real-worl
Multi-Scale Dissemination of Time Series Data
DEFF Research Database (Denmark)
Guo, Qingsong; Zhou, Yongluan; Su, Li
2013-01-01
In this paper, we consider the problem of continuous dissemination of time series data, such as sensor measurements, to a large number of subscribers. These subscribers fall into multiple subscription levels, where each subscription level is specified by the bandwidth constraint of a subscriber......, which is an abstract indicator for both the physical limits and the amount of data that the subscriber would like to handle. To handle this problem, we propose a system framework for multi-scale time series data dissemination that employs a typical tree-based dissemination network and existing time-series...
On the detection of superdiffusive behaviour in time series
Gottwald, Georg A
2016-01-01
We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data and relies on one realisation (ie one sample path) of the process. Linear drift effects are automatically removed without any preprocessing. We show numerical results for time series constructed from i.i.d. $\\alpha$-stable random variables and from deterministic weakly chaotic maps. We compare our method with the standard method of estimating the growth rate of the mean-square displacement as well as the $p$-variation method.
Genetic programming-based chaotic time series modeling
Institute of Scientific and Technical Information of China (English)
张伟; 吴智铭; 杨根科
2004-01-01
This paper proposes a Genetic Programming-Based Modeling(GPM)algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space,and the Particle Swarm Optimization(PSO)algorithm is used for Nonlinear Parameter Estimation(NPE)of dynamic model structures. In addition,GPM integrates the results of Nonlinear Time Series Analysis(NTSA)to adjust the parameters and takes them as the criteria of established models.Experiments showed the effectiveness of such improvements on chaotic time series modeling.
Algorithms for Linear Time Series Analysis: With R Package
Directory of Open Access Journals (Sweden)
A. Ian McLeod
2007-11-01
Full Text Available Our ltsa package implements the Durbin-Levinson and Trench algorithms and provides a general approach to the problems of fitting, forecasting and simulating linear time series models as well as fitting regression models with linear time series errors. For computational efficiency both algorithms are implemented in C and interfaced to R. Examples are given which illustrate the efficiency and accuracy of the algorithms. We provide a second package FGN which illustrates the use of the ltsa package with fractional Gaussian noise (FGN. It is hoped that the ltsa will provide a base for further time series software.
Modelling road accidents: An approach using structural time series
Junus, Noor Wahida Md; Ismail, Mohd Tahir
2014-09-01
In this paper, the trend of road accidents in Malaysia for the years 2001 until 2012 was modelled using a structural time series approach. The structural time series model was identified using a stepwise method, and the residuals for each model were tested. The best-fitted model was chosen based on the smallest Akaike Information Criterion (AIC) and prediction error variance. In order to check the quality of the model, a data validation procedure was performed by predicting the monthly number of road accidents for the year 2012. Results indicate that the best specification of the structural time series model to represent road accidents is the local level with a seasonal model.
Scalable Prediction of Energy Consumption using Incremental Time Series Clustering
Energy Technology Data Exchange (ETDEWEB)
Simmhan, Yogesh; Noor, Muhammad Usman
2013-10-09
Time series datasets are a canonical form of high velocity Big Data, and often generated by pervasive sensors, such as found in smart infrastructure. Performing predictive analytics on time series data can be computationally complex, and requires approximation techniques. In this paper, we motivate this problem using a real application from the smart grid domain. We propose an incremental clustering technique, along with a novel affinity score for determining cluster similarity, which help reduce the prediction error for cumulative time series within a cluster. We evaluate this technique, along with optimizations, using real datasets from smart meters, totaling ~700,000 data points, and show the efficacy of our techniques in improving the prediction error of time series data within polynomial time.
Energy Technology Data Exchange (ETDEWEB)
Shapoval, A. [Financial University under the Government of the Russian Federation, Leningradsky pr. 49, Moscow (Russian Federation); Le Mouël, J.-L.; Courtillot, V. [Institute de Physique du Globe, Sorbonne Paris Cité, Paris (France); Shnirman, M. [Institute of Earthquake Prediction Theory and Mathematical Geophysics, Profsoyuznaya 84/32, 117997 Moscow (Russian Federation)
2015-01-20
The irregularity index λ is applied to the high-frequency content of daily sunspot numbers ISSN. This λ is a modification of the standard maximal Lyapunov exponent. It is computed here as a function of embedding dimension m, within four-year time windows centered at the maxima of Schwabe cycles. The λ(m) curves form separate clusters (pre-1923 and post-1933). This supports a regime transition and narrows its occurrence to cycle 16, preceding the growth of activity leading to the Modern Maximum. The two regimes are reproduced by a simple autoregressive process AR(1), with the mean of Poisson noise undergoing 11 yr modulation. The autocorrelation a of the process (linked to sunspot lifetime) is a ≈ 0.8 for 1850-1923 and ≈0.95 for 1933-2013. The AR(1) model suggests that groups of spots appear with a Poisson rate and disappear at a constant rate. We further applied the irregularity index to the daily sunspot group number series for the northern and southern hemispheres, provided by the Greenwich Royal Observatory (RGO), in order to study a possible desynchronization. Correlations between the north and south λ(m) curves vary quite strongly with time and indeed show desynchronization. This may reflect a slow change in the dimension of an underlying dynamical system. The ISSN and RGO series of group numbers do not imply an identical mechanism, but both uncover a regime change at a similar time. Computation of the irregularity index near the maximum of cycle 24 will help in checking whether yet another regime change is under way.
Comparison of sunspot properties in cycles 23 and 24
Rezaei, Reza; Schmidt, Wolfgang; Beck, Christian
Sunspots form by coalescence of small-scale magnetic elements and pores in magnetic flux emergence areas. By observing recently formed sunspots just after their initial growth and before substantial decay, one samples a magnetic signal which has been least disturbed by granulation. Properties of the emergence events have a direct impact on the results. Failed active regions, e.g. the ones which cannot form a sunspot, are a clear example: in several cases, they would harbor enough magnetic flux to form a small sunspot but fail to do so. Another way to evaluate secular variations of flux emergence events is to quantify long-term trends of sunspot properties. The 11-year solar magnetic activity cycle has been known for centuries. During this time the activity level changed dramatically from the Maunder minimum (1650-1700) to the Modern maximum in mid 20-th century. The extended minimum of the last solar cycle alerted solar physicist about possible long-term variation in the solar magnetic activity. While some argue that the Sun was unusually active in mid 20-th century, others find it unusually inactive now. This caused speculations whether the solar activity cycle is overlaid with a long-term decline that may lead to another grand minimum in the near future. Some extrapolations predicted that there will be no sunspots in the next cycle. Detailed observations of sunspot properties were performed only in the last few cycles. Such spectropolarimetric observations enable us to accurately derive the magnetic field strengths of spots and their physical properties. We present measurements of sunspot intensity, area, and magnetic field strength and compare the present cycle 24 with the previous one. We analyze a sample of about 400 sunspots observed from 1999 until 2014 with the Tenerife Infrared Polarimeter at the German Vacuum Tower Telescope as well as with the Facility Infrared Spectropolarimeter of the Dunn Solar Telescope of the NSO. The magnetic field strength is
Quantifying memory in complex physiological time-series.
Shirazi, Amir H; Raoufy, Mohammad R; Ebadi, Haleh; De Rui, Michele; Schiff, Sami; Mazloom, Roham; Hajizadeh, Sohrab; Gharibzadeh, Shahriar; Dehpour, Ahmad R; Amodio, Piero; Jafari, G Reza; Montagnese, Sara; Mani, Ali R
2013-01-01
In a time-series, memory is a statistical feature that lasts for a period of time and distinguishes the time-series from a random, or memory-less, process. In the present study, the concept of "memory length" was used to define the time period, or scale over which rare events within a physiological time-series do not appear randomly. The method is based on inverse statistical analysis and provides empiric evidence that rare fluctuations in cardio-respiratory time-series are 'forgotten' quickly in healthy subjects while the memory for such events is significantly prolonged in pathological conditions such as asthma (respiratory time-series) and liver cirrhosis (heart-beat time-series). The memory length was significantly higher in patients with uncontrolled asthma compared to healthy volunteers. Likewise, it was significantly higher in patients with decompensated cirrhosis compared to those with compensated cirrhosis and healthy volunteers. We also observed that the cardio-respiratory system has simple low order dynamics and short memory around its average, and high order dynamics around rare fluctuations.
Elements of nonlinear time series analysis and forecasting
De Gooijer, Jan G
2017-01-01
This book provides an overview of the current state-of-the-art of nonlinear time series analysis, richly illustrated with examples, pseudocode algorithms and real-world applications. Avoiding a “theorem-proof” format, it shows concrete applications on a variety of empirical time series. The book can be used in graduate courses in nonlinear time series and at the same time also includes interesting material for more advanced readers. Though it is largely self-contained, readers require an understanding of basic linear time series concepts, Markov chains and Monte Carlo simulation methods. The book covers time-domain and frequency-domain methods for the analysis of both univariate and multivariate (vector) time series. It makes a clear distinction between parametric models on the one hand, and semi- and nonparametric models/methods on the other. This offers the reader the option of concentrating exclusively on one of these nonlinear time series analysis methods. To make the book as user friendly as possible...
The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae
Indian Academy of Sciences (India)
L. H. Deng; J. Y. Song; Y. Y. Xiang; Y. K. Tang
2011-09-01
The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).
Phase analysis of sunspot group numbers on both solar hemispheres
Institute of Scientific and Technical Information of China (English)
Lin-Hua Deng; Zhong-Quan Qu; Xiao-Li Yan; Kai-Rang Wang
2013-01-01
Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres.It is found that (1) the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one,which should lead to phase asynchrony between them but with a slight effect; (2) the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other,and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one; (3) the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874-1927,after which,the southern hemisphere leads the northern hemisphere in the years 1928-1964,and then the northern hemisphere leads in time till the present.
Rodgers, Joseph Lee; Beasley, William Howard; Schuelke, Matthew
2014-01-01
Many data structures, particularly time series data, are naturally seasonal, cyclical, or otherwise circular. Past graphical methods for time series have focused on linear plots. In this article, we move graphical analysis onto the circle. We focus on 2 particular methods, one old and one new. Rose diagrams are circular histograms and can be produced in several different forms using the RRose software system. In addition, we propose, develop, illustrate, and provide software support for a new circular graphical method, called Wrap-Around Time Series Plots (WATS Plots), which is a graphical method useful to support time series analyses in general but in particular in relation to interrupted time series designs. We illustrate the use of WATS Plots with an interrupted time series design evaluating the effect of the Oklahoma City bombing on birthrates in Oklahoma County during the 10 years surrounding the bombing of the Murrah Building in Oklahoma City. We compare WATS Plots with linear time series representations and overlay them with smoothing and error bands. Each method is shown to have advantages in relation to the other; in our example, the WATS Plots more clearly show the existence and effect size of the fertility differential.
Multi-dimensional sparse time series: feature extraction
Franciosi, Marco
2008-01-01
We show an analysis of multi-dimensional time series via entropy and statistical linguistic techniques. We define three markers encoding the behavior of the series, after it has been translated into a multi-dimensional symbolic sequence. The leading component and the trend of the series with respect to a mobile window analysis result from the entropy analysis and label the dynamical evolution of the series. The diversification formalizes the differentiation in the use of recurrent patterns, from a Zipf law point of view. These markers are the starting point of further analysis such as classification or clustering of large database of multi-dimensional time series, prediction of future behavior and attribution of new data. We also present an application to economic data. We deal with measurements of money investments of some business companies in advertising market for different media sources.
EUV Sunspot Plumes Observed with SOHO
Maltby, P; Brekke, P; Haugan, S V H; Kjeldseth-Moe, O; Wikstøl, O; Rimmele, T R; Wikstøl, O
1998-01-01
Bright EUV sunspot plumes have been observed in five out of nine sunspot regions with the Coronal Diagnostic Spectrometer -- CDS on SOHO. In the other four regions the brightest line emissions may appear inside the sunspot but are mainly concentrated in small regions outside the sunspot areas. These results are in contrast to those obtained during the Solar Maximum Mission, but are compatible with the Skylab mission results. The present observations show that sunspot plumes are formed in the upper part of the transition region, occur both in magnetic unipolar-- and bipolar regions, and may extend from the umbra into the penumbra.
A probability distribution approach to synthetic turbulence time series
Sinhuber, Michael; Bodenschatz, Eberhard; Wilczek, Michael
2016-11-01
The statistical features of turbulence can be described in terms of multi-point probability density functions (PDFs). The complexity of these statistical objects increases rapidly with the number of points. This raises the question of how much information has to be incorporated into statistical models of turbulence to capture essential features such as inertial-range scaling and intermittency. Using high Reynolds number hot-wire data obtained at the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, we establish a PDF-based approach on generating synthetic time series that reproduce those features. To do this, we measure three-point conditional PDFs from the experimental data and use an adaption-rejection method to draw random velocities from this distribution to produce synthetic time series. Analyzing these synthetic time series, we find that time series based on even low-dimensional conditional PDFs already capture some essential features of real turbulent flows.
On robust forecasting of autoregressive time series under censoring
Kharin, Y.; Badziahin, I.
2009-01-01
Problems of robust statistical forecasting are considered for autoregressive time series observed under distortions generated by interval censoring. Three types of robust forecasting statistics are developed; meansquare risk is evaluated for the developed forecasting statistics. Numerical results are given.
Lagrangian Time Series Models for Ocean Surface Drifter Trajectories
Sykulski, Adam M; Lilly, Jonathan M; Danioux, Eric
2016-01-01
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer important physical parameters of inertial oscillations and other ocean processes. Nonstationary time series methods are employed to account for the spatiotemporal variability of each trajectory. Because the datasets are large, we construct computationally efficient methods through the use of frequency-domain modelling and estimation, with the data expressed as complex-valued time series. We detail how practical issues related to sampling and model misspecification may be addressed using semi-parametric techniques for time series, and we demonstrate the effectiveness of our stochastic models through application to both real-world data and to numerical model output.
Fast and Flexible Multivariate Time Series Subsequence Search
National Aeronautics and Space Administration — Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical...
AFSC/ABL: Ugashik sockeye salmon scale time series
National Oceanic and Atmospheric Administration, Department of Commerce — A time series of scale samples (1956 b?? 2002) collected from adult sockeye salmon returning to Ugashik River were retrieved from the Alaska Department of Fish and...
On robust forecasting of autoregressive time series under censoring
Kharin, Y.; Badziahin, I.
2009-01-01
Problems of robust statistical forecasting are considered for autoregressive time series observed under distortions generated by interval censoring. Three types of robust forecasting statistics are developed; meansquare risk is evaluated for the developed forecasting statistics. Numerical results are given.
Multivariate Time Series Analysis for Optimum Production Forecast ...
African Journals Online (AJOL)
FIRST LADY
Keywords: production model, inventory management, multivariate time series ... regard when companies over stock raw materials inventory as a result of .... Error Analysis for Forecasts of 2008-2014 to Establish Model out of. Control.
Phenotyping of Clinical Time Series with LSTM Recurrent Neural Networks
Lipton, Zachary C.; Kale, David C.; Wetzell, Randall C.
2015-01-01
We present a novel application of LSTM recurrent neural networks to multilabel classification of diagnoses given variable-length time series of clinical measurements. Our method outperforms a strong baseline on a variety of metrics.
Distinguishing chaotic time series from noise: A random matrix approach
Ye, Bin; Chen, Jianxing; Ju, Chen; Li, Huijun; Wang, Xuesong
2017-03-01
Deterministically chaotic systems can often give rise to random and unpredictable behaviors which make the time series obtained from them to be almost indistinguishable from noise. Motivated by the fact that data points in a chaotic time series will have intrinsic correlations between them, we propose a random matrix theory (RMT) approach to identify the deterministic or stochastic dynamics of the system. We show that the spectral distributions of the correlation matrices, constructed from the chaotic time series, deviate significantly from the predictions of random matrix ensembles. On the contrary, the eigenvalue statistics for a noisy signal follow closely those of random matrix ensembles. Numerical results also indicate that the approach is to some extent robust to additive observational noise which pollutes the data in many practical situations. Our approach is efficient in recognizing the continuous chaotic dynamics underlying the evolution of the time series.
Unsupervised land cover change detection: meaningful sequential time series analysis
CSIR Research Space (South Africa)
Salmon, BP
2011-06-01
Full Text Available An automated land cover change detection method is proposed that uses coarse spatial resolution hyper-temporal earth observation satellite time series data. The study compared three different unsupervised clustering approaches that operate on short...
AFSC/ABL: Naknek sockeye salmon scale time series
National Oceanic and Atmospheric Administration, Department of Commerce — A time series of scale samples (1956 2002) collected from adult sockeye salmon returning to Naknek River were retrieved from the Alaska Department of Fish and Game....
A Generalization of Some Classical Time Series Tools
DEFF Research Database (Denmark)
Nielsen, Henrik Aalborg; Madsen, Henrik
2001-01-01
In classical time series analysis the sample autocorrelation function (SACF) and the sample partial autocorrelation function (SPACF) has gained wide application for structural identification of linear time series models. We suggest generalizations, founded on smoothing techniques, applicable for ....... In this paper the generalizations are applied to some simulated data sets and to the Canadian lynx data. The generalizations seem to perform well and the measure of the departure from linearity proves to be an important additional tool....
Outlier detection algorithms for least squares time series regression
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
We review recent asymptotic results on some robust methods for multiple regression. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator...... theory involves normal distribution results and Poisson distribution results. The theory is applied to a time series data set....
The use of synthetic input sequences in time series modeling
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Dair Jose de [Programa de Pos-Graduacao em Engenharia Eletrica, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31.270-901 Belo Horizonte, MG (Brazil); Letellier, Christophe [CORIA/CNRS UMR 6614, Universite et INSA de Rouen, Av. de l' Universite, BP 12, F-76801 Saint-Etienne du Rouvray cedex (France); Gomes, Murilo E.D. [Programa de Pos-Graduacao em Engenharia Eletrica, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31.270-901 Belo Horizonte, MG (Brazil); Aguirre, Luis A. [Programa de Pos-Graduacao em Engenharia Eletrica, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 31.270-901 Belo Horizonte, MG (Brazil)], E-mail: aguirre@cpdee.ufmg.br
2008-08-04
In many situations time series models obtained from noise-like data settle to trivial solutions under iteration. This Letter proposes a way of producing a synthetic (dummy) input, that is included to prevent the model from settling down to a trivial solution, while maintaining features of the original signal. Simulated benchmark models and a real time series of RR intervals from an ECG are used to illustrate the procedure.
The use of synthetic input sequences in time series modeling
de Oliveira, Dair José; Letellier, Christophe; Gomes, Murilo E. D.; Aguirre, Luis A.
2008-08-01
In many situations time series models obtained from noise-like data settle to trivial solutions under iteration. This Letter proposes a way of producing a synthetic (dummy) input, that is included to prevent the model from settling down to a trivial solution, while maintaining features of the original signal. Simulated benchmark models and a real time series of RR intervals from an ECG are used to illustrate the procedure.
Prediction and interpolation of time series by state space models
Helske, Jouni
2015-01-01
A large amount of data collected today is in the form of a time series. In order to make realistic inferences based on time series forecasts, in addition to point predictions, prediction intervals or other measures of uncertainty should be presented. Multiple sources of uncertainty are often ignored due to the complexities involved in accounting them correctly. In this dissertation, some of these problems are reviewed and some new solutions are presented. A state space approach...
Stacked Heterogeneous Neural Networks for Time Series Forecasting
Directory of Open Access Journals (Sweden)
Florin Leon
2010-01-01
Full Text Available A hybrid model for time series forecasting is proposed. It is a stacked neural network, containing one normal multilayer perceptron with bipolar sigmoid activation functions, and the other with an exponential activation function in the output layer. As shown by the case studies, the proposed stacked hybrid neural model performs well on a variety of benchmark time series. The combination of weights of the two stack components that leads to optimal performance is also studied.
Mean shifts, unit roots and forecasting seasonal time series
Franses, Philip Hans; Paap, Richard; Hoek, Henk
1997-01-01
textabstractExamples of descriptive models for changing seasonal patterns in economic time series are autoregressive models with seasonal unit roots or with deterministic seasonal mean shifts. In this paper we show through a forecasting comparison for three macroeconomic time series (for which tests indicate the presence of seasonal unit roots) that allowing for possible seasonal mean shifts can improve forecast performance. Next, by means of simulation we demonstrate the impact of imposing a...
Extracting Chaos Control Parameters from Time Series Analysis
Energy Technology Data Exchange (ETDEWEB)
Santos, R B B [Centro Universitario da FEI, Avenida Humberto de Alencar Castelo Branco 3972, 09850-901, Sao Bernardo do Campo, SP (Brazil); Graves, J C, E-mail: rsantos@fei.edu.br [Instituto Tecnologico de Aeronautica, Praca Marechal Eduardo Gomes 50, 12228-900, Sao Jose dos Campos, SP (Brazil)
2011-03-01
We present a simple method to analyze time series, and estimate the parameters needed to control chaos in dynamical systems. Application of the method to a system described by the logistic map is also shown. Analyzing only two 100-point time series, we achieved results within 2% of the analytical ones. With these estimates, we show that OGY control method successfully stabilized a period-1 unstable periodic orbit embedded in the chaotic attractor.
Time Series Analysis of Insar Data: Methods and Trends
Osmanoglu, Batuhan; Sunar, Filiz; Wdowinski, Shimon; Cano-Cabral, Enrique
2015-01-01
Time series analysis of InSAR data has emerged as an important tool for monitoring and measuring the displacement of the Earth's surface. Changes in the Earth's surface can result from a wide range of phenomena such as earthquakes, volcanoes, landslides, variations in ground water levels, and changes in wetland water levels. Time series analysis is applied to interferometric phase measurements, which wrap around when the observed motion is larger than one-half of the radar wavelength. Thus, the spatio-temporal ''unwrapping" of phase observations is necessary to obtain physically meaningful results. Several different algorithms have been developed for time series analysis of InSAR data to solve for this ambiguity. These algorithms may employ different models for time series analysis, but they all generate a first-order deformation rate, which can be compared to each other. However, there is no single algorithm that can provide optimal results in all cases. Since time series analyses of InSAR data are used in a variety of applications with different characteristics, each algorithm possesses inherently unique strengths and weaknesses. In this review article, following a brief overview of InSAR technology, we discuss several algorithms developed for time series analysis of InSAR data using an example set of results for measuring subsidence rates in Mexico City.
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
FEI WanChun; BAI Lun
2009-01-01
In this paper,autocovariance nonstationary time series is clearly defined on a family of time series.We propose three types of TVPAR (time-varying parameter auto-regressive) models:the full order TVPAR model,the time-unvarying order TVPAR model and the time-varying order TVPAR model for autocovariance nonstationary time series.Related minimum AIC (Akaike information criterion) estimations are carried out.
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.
Detection of Emerging Sunspot Regions in the Solar Interior
Ilonidis, Stathis; Zhao, Junwei; Kosovichev, Alexander
2011-08-01
Sunspots are regions where strong magnetic fields emerge from the solar interior and where major eruptive events occur. These energetic events can cause power outages, interrupt telecommunication and navigation services, and pose hazards to astronauts. We detected subsurface signatures of emerging sunspot regions before they appeared on the solar disc. Strong acoustic travel-time anomalies of an order of 12 to 16 seconds were detected as deep as 65,000 kilometers. These anomalies were associated with magnetic structures that emerged with an average speed of 0.3 to 0.6 kilometer per second and caused high peaks in the photospheric magnetic flux rate 1 to 2 days after the detection of the anomalies. Thus, synoptic imaging of subsurface magnetic activity may allow anticipation of large sunspot regions before they become visible, improving space weather forecast.
The Effect of Sunspot Weighting
Svalgaard, Leif; Cortesi, Sergio
2015-01-01
Waldmeier in 1947 introduced a weighting (on a scale from 1 to 5) of the sunspot count made at Zurich and its auxiliary station Locarno, whereby larger spots were counted more than once. This counting method inflates the relative sunspot number over that which corresponds to the scale set by Wolfer and Brunner. Svalgaard re-counted some 60,000 sunspots on drawings from the reference station Locarno and determined that the number of sunspots reported were 'over counted' by 44% on average, leading to an inflation (measured by a weight factor) in excess of 1.2 for high solar activity. In a double-blind parallel counting by the Locarno observer Cagnotti, we determined that Svalgaard's count closely matches that of Cagnotti's, allowing us to determine the daily weight factor since 2003 (and sporadically before). We find that a simple empirical equation fits the observed weight factors well, and use that fit to estimate the weight factor for each month back to the introduction of weighting in 1947 and thus to be ab...
A method for detecting changes in long time series
Energy Technology Data Exchange (ETDEWEB)
Downing, D.J.; Lawkins, W.F.; Morris, M.D.; Ostrouchov, G.
1995-09-01
Modern scientific activities, both physical and computational, can result in time series of many thousands or even millions of data values. Here the authors describe a statistically motivated algorithm for quick screening of very long time series data for the presence of potentially interesting but arbitrary changes. The basic data model is a stationary Gaussian stochastic process, and the approach to detecting a change is the comparison of two predictions of the series at a time point or contiguous collection of time points. One prediction is a ``forecast``, i.e. based on data from earlier times, while the other a ``backcast``, i.e. based on data from later times. The statistic is the absolute value of the log-likelihood ratio for these two predictions, evaluated at the observed data. A conservative procedure is suggested for specifying critical values for the statistic under the null hypothesis of ``no change``.
Combined forecasts from linear and nonlinear time series models
N. Terui (Nobuhiko); H.K. van Dijk (Herman)
1999-01-01
textabstractCombined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)line
LEGENDRE SERIES SOLUTIONS FOR TIME-VARIATION DYNAMICS
Institute of Scientific and Technical Information of China (English)
Cao Zhiyuan; Zou Guiping; Tang Shougao
2000-01-01
In this topic, a new approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established, which is beneficial to further research of time-variation science.
Similarity estimators for irregular and age-uncertain time series
Rehfeld, K.; Kurths, J.
2014-01-01
Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60-55% (in the linear case) to 53-42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity
Similarity estimators for irregular and age uncertain time series
Rehfeld, K.; Kurths, J.
2013-09-01
Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many datasets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age uncertain time series. We compare the Gaussian-kernel based cross correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60-55% (in the linear case) to 53-42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity
Comparison of time series using entropy and mutual correlation
Madonna, Fabio; Rosoldi, Marco
2015-04-01
The potential for redundant time series to reduce uncertainty in atmospheric variables has not been investigated comprehensively for climate observations. Moreover, comparison among time series of in situ and ground based remote sensing measurements have been performed using several methods, but quite often relying on linear models. In this work, the concepts of entropy (H) and mutual correlation (MC), defined in the frame of the information theory, are applied to the study of essential climate variables with the aim of characterizing the uncertainty of a time series and the redundancy of collocated measurements provided by different surface-based techniques. In particular, integrated water vapor (IWV) and water vapour mixing ratio times series obtained at five highly instrumented GRUAN (GCOS, Global Climate Observing System, Reference Upper-Air Network) stations with several sensors (e.g radiosondes, GPS, microwave and infrared radiometers, Raman lidar), in the period from 2010-2012, are analyzed in terms of H and MC. The comparison between the probability density functions of the time series shows that caution in using linear assumptions is needed and the use of statistics, like entropy, that are robust to outliers, is recommended to investigate measurements time series. Results reveals that the random uncertainties on the IWV measured with radiosondes, global positioning system, microwave and infrared radiometers, and Raman lidar measurements differed by less than 8 % over the considered time period. Comparisons of the time series of IWV content from ground-based remote sensing instruments with in situ soundings showed that microwave radiometers have the highest redundancy with the IWV time series measured by radiosondes and therefore the highest potential to reduce the random uncertainty of the radiosondes time series. Moreover, the random uncertainty of a time series from one instrument can be reduced by 60% by constraining the measurements with those from
Similarity estimators for irregular and age uncertain time series
Directory of Open Access Journals (Sweden)
K. Rehfeld
2013-09-01
Full Text Available Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many datasets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age uncertain time series. We compare the Gaussian-kernel based cross correlation (gXCF, Rehfeld et al., 2011 and mutual information (gMI, Rehfeld et al., 2013 against their interpolation-based counterparts and the new event synchronization function (ESF. We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case to 53–42% (for the nonlinear processes of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time
Analyses of Inhomogeneities in Radiosonde Temperature and Humidity Time Series.
Zhai, Panmao; Eskridge, Robert E.
1996-04-01
Twice daily radiosonde data from selected stations in the United States (period 1948 to 1990) and China (period 1958 to 1990) were sorted into time series. These stations have one sounding taken in darkness and the other in sunlight. The analysis shows that the 0000 and 1200 UTC time series are highly correlated. Therefore, the Easterling and Peterson technique was tested on the 0000 and 1200 time series to detect inhomogeneities and to estimate the size of the biases. Discontinuities were detected using the difference series created from the 0000 and 1200 UTC time series. To establish that the detected bias was significant, a t test was performed to confirm that the change occurs in the daytime series but not in the nighttime series.Both U.S. and Chinese radiosonde temperature and humidity data include inhomogeneities caused by changes in radiosonde sensors and observation times. The U.S. humidity data have inhomogeneities that were caused by instrument changes and the censoring of data. The practice of reporting relative humidity as 19% when it is lower than 20% or the temperature is below 40°C is called censoring. This combination of procedural and instrument changes makes the detection of biases and adjustment of the data very difficult. In the Chinese temperatures, them are inhomogeneities related to a change in the radiation correction procedure.Test results demonstrate that a modified Easterling and Peterson method is suitable for use in detecting and adjusting time series radiosonde data.Accurate stations histories are very desirable. Stations histories can confirm that detected inhomogeneities are related to instrument or procedural changes. Adjustments can then he made to the data with some confidence.
Normalization of sunspot cycles and eigen mode analysis
Institute of Scientific and Technical Information of China (English)
徐文耀
2002-01-01
The smoothed monthly sunspot numbers of the previous 22 complete sunspot cycles are normalized in time domain, and then an eigen mode analysis is carried out to draw the principle factors (or components) in the cycles. The results show that the main characteristics of the solar cycles can be described fairly well by the first 5 eigen modes. The obtained eigen modes are used to predict the declining phase of cycle 23 on the basis of the data prior to its maximum. The prediction indicates that cycle 23 will last for 127 months to December 2006, with the minimum of 6.2.
Multiresolution analysis of Bursa Malaysia KLCI time series
Ismail, Mohd Tahir; Dghais, Amel Abdoullah Ahmed
2017-05-01
In general, a time series is simply a sequence of numbers collected at regular intervals over a period. Financial time series data processing is concerned with the theory and practice of processing asset price over time, such as currency, commodity data, and stock market data. The primary aim of this study is to understand the fundamental characteristics of selected financial time series by using the time as well as the frequency domain analysis. After that prediction can be executed for the desired system for in sample forecasting. In this study, multiresolution analysis which the assist of discrete wavelet transforms (DWT) and maximal overlap discrete wavelet transform (MODWT) will be used to pinpoint special characteristics of Bursa Malaysia KLCI (Kuala Lumpur Composite Index) daily closing prices and return values. In addition, further case study discussions include the modeling of Bursa Malaysia KLCI using linear ARIMA with wavelets to address how multiresolution approach improves fitting and forecasting results.
Correlation measure to detect time series distances, whence economy globalization
Miśkiewicz, Janusz; Ausloos, Marcel
2008-11-01
An instantaneous time series distance is defined through the equal time correlation coefficient. The idea is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation. Some data discussion is first presented to decide what (EKS, GK, or derived) GDP series should be studied. Distances are then calculated from the correlation coefficient values between pairs of series. The role of time averaging of the distances over finite size windows is discussed. Three network structures are next constructed based on the hierarchy of distances. It is shown that the mean distance between the most developed countries on several networks actually decreases in time, -which we consider as a proof of globalization. An empirical law is found for the evolution after 1990, similar to that found in flux creep. The optimal observation time window size is found ≃15 years.
Exploratory Causal Analysis in Bivariate Time Series Data
McCracken, James M.
Many scientific disciplines rely on observational data of systems for which it is difficult (or impossible) to implement controlled experiments and data analysis techniques are required for identifying causal information and relationships directly from observational data. This need has lead to the development of many different time series causality approaches and tools including transfer entropy, convergent cross-mapping (CCM), and Granger causality statistics. In this thesis, the existing time series causality method of CCM is extended by introducing a new method called pairwise asymmetric inference (PAI). It is found that CCM may provide counter-intuitive causal inferences for simple dynamics with strong intuitive notions of causality, and the CCM causal inference can be a function of physical parameters that are seemingly unrelated to the existence of a driving relationship in the system. For example, a CCM causal inference might alternate between ''voltage drives current'' and ''current drives voltage'' as the frequency of the voltage signal is changed in a series circuit with a single resistor and inductor. PAI is introduced to address both of these limitations. Many of the current approaches in the times series causality literature are not computationally straightforward to apply, do not follow directly from assumptions of probabilistic causality, depend on assumed models for the time series generating process, or rely on embedding procedures. A new approach, called causal leaning, is introduced in this work to avoid these issues. The leaning is found to provide causal inferences that agree with intuition for both simple systems and more complicated empirical examples, including space weather data sets. The leaning may provide a clearer interpretation of the results than those from existing time series causality tools. A practicing analyst can explore the literature to find many proposals for identifying drivers and causal connections in times series data
Evaluation of scaling invariance embedded in short time series.
Pan, Xue; Hou, Lei; Stephen, Mutua; Yang, Huijie; Zhu, Chenping
2014-01-01
Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2). Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03) and sharp confidential interval (standard deviation ≤0.05). Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.
Evaluation of scaling invariance embedded in short time series.
Directory of Open Access Journals (Sweden)
Xue Pan
Full Text Available Scaling invariance of time series has been making great contributions in diverse research fields. But how to evaluate scaling exponent from a real-world series is still an open problem. Finite length of time series may induce unacceptable fluctuation and bias to statistical quantities and consequent invalidation of currently used standard methods. In this paper a new concept called correlation-dependent balanced estimation of diffusion entropy is developed to evaluate scale-invariance in very short time series with length ~10(2. Calculations with specified Hurst exponent values of 0.2,0.3,...,0.9 show that by using the standard central moving average de-trending procedure this method can evaluate the scaling exponents for short time series with ignorable bias (≤0.03 and sharp confidential interval (standard deviation ≤0.05. Considering the stride series from ten volunteers along an approximate oval path of a specified length, we observe that though the averages and deviations of scaling exponents are close, their evolutionary behaviors display rich patterns. It has potential use in analyzing physiological signals, detecting early warning signals, and so on. As an emphasis, the our core contribution is that by means of the proposed method one can estimate precisely shannon entropy from limited records.
Statistical modelling of agrometeorological time series by exponential smoothing
Murat, Małgorzata; Malinowska, Iwona; Hoffmann, Holger; Baranowski, Piotr
2016-01-01
Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, long-term meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
Discovering shared and individual latent structure in multiple time series
Saria, Suchi; Penn, Anna
2010-01-01
This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant individual variability. Our method builds on the framework of latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet processes, which allows us to characterize each series as switching between latent ``topics'', where each topic is characterized as a distribution over ``words'' that specify the series dynamics. However, unlike standard applications of LDA, we discover the words as we learn the model. We apply this model to the task of tracking the physiological signals of premature infants; our model obtains clinically significant insights as well as useful features for supervised learning tasks.
Self-affinity in the dengue fever time series
Azevedo, S. M.; Saba, H.; Miranda, J. G. V.; Filho, A. S. Nascimento; Moret, M. A.
2016-06-01
Dengue is a complex public health problem that is common in tropical and subtropical regions. This disease has risen substantially in the last three decades, and the physical symptoms depict the self-affine behavior of the occurrences of reported dengue cases in Bahia, Brazil. This study uses detrended fluctuation analysis (DFA) to verify the scale behavior in a time series of dengue cases and to evaluate the long-range correlations that are characterized by the power law α exponent for different cities in Bahia, Brazil. The scaling exponent (α) presents different long-range correlations, i.e. uncorrelated, anti-persistent, persistent and diffusive behaviors. The long-range correlations highlight the complex behavior of the time series of this disease. The findings show that there are two distinct types of scale behavior. In the first behavior, the time series presents a persistent α exponent for a one-month period. For large periods, the time series signal approaches subdiffusive behavior. The hypothesis of the long-range correlations in the time series of the occurrences of reported dengue cases was validated. The observed self-affinity is useful as a forecasting tool for future periods through extrapolation of the α exponent behavior. This complex system has a higher predictability in a relatively short time (approximately one month), and it suggests a new tool in epidemiological control strategies. However, predictions for large periods using DFA are hidden by the subdiffusive behavior.
Drunk driving detection based on classification of multivariate time series.
Li, Zhenlong; Jin, Xue; Zhao, Xiaohua
2015-09-01
This paper addresses the problem of detecting drunk driving based on classification of multivariate time series. First, driving performance measures were collected from a test in a driving simulator located in the Traffic Research Center, Beijing University of Technology. Lateral position and steering angle were used to detect drunk driving. Second, multivariate time series analysis was performed to extract the features. A piecewise linear representation was used to represent multivariate time series. A bottom-up algorithm was then employed to separate multivariate time series. The slope and time interval of each segment were extracted as the features for classification. Third, a support vector machine classifier was used to classify driver's state into two classes (normal or drunk) according to the extracted features. The proposed approach achieved an accuracy of 80.0%. Drunk driving detection based on the analysis of multivariate time series is feasible and effective. The approach has implications for drunk driving detection. Copyright © 2015 Elsevier Ltd and National Safety Council. All rights reserved.
Wavelet matrix transform for time-series similarity measurement
Institute of Scientific and Technical Information of China (English)
HU Zhi-kun; XU Fei; GUI Wei-hua; YANG Chun-hua
2009-01-01
A time-series similarity measurement method based on wavelet and matrix transform was proposed, and its anti-noise ability, sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace, and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example, the experimental results show that the proposed method has low dimension of feature vector, the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method, the sensitivity of proposed method is 1/3 as large as that of plain wavelet method, and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases.
Stochastic modeling of hourly rainfall times series in Campania (Italy)
Giorgio, M.; Greco, R.
2009-04-01
Occurrence of flowslides and floods in small catchments is uneasy to predict, since it is affected by a number of variables, such as mechanical and hydraulic soil properties, slope morphology, vegetation coverage, rainfall spatial and temporal variability. Consequently, landslide risk assessment procedures and early warning systems still rely on simple empirical models based on correlation between recorded rainfall data and observed landslides and/or river discharges. Effectiveness of such systems could be improved by reliable quantitative rainfall prediction, which can allow gaining larger lead-times. Analysis of on-site recorded rainfall height time series represents the most effective approach for a reliable prediction of local temporal evolution of rainfall. Hydrological time series analysis is a widely studied field in hydrology, often carried out by means of autoregressive models, such as AR, ARMA, ARX, ARMAX (e.g. Salas [1992]). Such models gave the best results when applied to the analysis of autocorrelated hydrological time series, like river flow or level time series. Conversely, they are not able to model the behaviour of intermittent time series, like point rainfall height series usually are, especially when recorded with short sampling time intervals. More useful for this issue are the so-called DRIP (Disaggregated Rectangular Intensity Pulse) and NSRP (Neymann-Scott Rectangular Pulse) model [Heneker et al., 2001; Cowpertwait et al., 2002], usually adopted to generate synthetic point rainfall series. In this paper, the DRIP model approach is adopted, in which the sequence of rain storms and dry intervals constituting the structure of rainfall time series is modeled as an alternating renewal process. Final aim of the study is to provide a useful tool to implement an early warning system for hydrogeological risk management. Model calibration has been carried out with hourly rainfall hieght data provided by the rain gauges of Campania Region civil
Stationary Time Series Analysis Using Information and Spectral Analysis
1992-09-01
spectral density function of the time series. The spectral density function f(w), 0 < w < 1, is defined as the Fourier transform of...series with spectral density function f(w). 4 An important result of Pinsker [(1964), p. 196] can be interpreted as providing a for- mula for asymptotic...Analysis Papers, Holden-Day, San Francisco, California. Parzen, E. (1958) "On asymptotically efficient consistent estimates of the spectral density function
Gaussian semiparametric estimation of non-stationary time series
Velasco, Carlos
1998-01-01
Generalizing the definition of the memory parameter d in terms of the differentiated series, we showed in Velasco (Non-stationary log-periodogram regression, Forthcoming J. Economet., 1997) that it is possible to estimate consistently the memory of non-stationary processes using methods designed for stationary long-range-dependent time series. In this paper we consider the Gaussian semiparametric estimate analysed by Robinson (Gaussian semiparametric estimation of long range dependence. Ann. ...
Moderate Growth Time Series for Dynamic Combinatorics Modelisation
Jaff, Luaï; Kacem, Hatem Hadj; Bertelle, Cyrille
2007-01-01
Here, we present a family of time series with a simple growth constraint. This family can be the basis of a model to apply to emerging computation in business and micro-economy where global functions can be expressed from local rules. We explicit a double statistics on these series which allows to establish a one-to-one correspondence between three other ballot-like strunctures.
First time-series optical photometry from Antarctica
Strassmeier, K G; Granzer, T; Tosti, G; DiVarano, I; Savanov, I; Bagaglia, M; Castellini, S; Mancini, A; Nucciarelli, G; Straniero, O; Distefano, E; Messina, S; Cutispoto, G
2008-01-01
Beating the Earth's day-night cycle is mandatory for long and continuous time-series photometry and had been achieved with either large ground-based networks of observatories at different geographic longitudes or when conducted from space. A third possibility is offered by a polar location with astronomically-qualified site characteristics. Aims. In this paper, we present the first scientific stellar time-series optical photometry from Dome C in Antarctica and analyze approximately 13,000 CCD frames taken in July 2007. We conclude that high-precision CCD photometry with exceptional time coverage and cadence can be obtained at Dome C in Antarctica and be successfully used for time-series astrophysics.
Time series analysis of the response of measurement instruments
Georgakaki, Dimitra; Polatoglou, Hariton
2012-01-01
In this work the significance of treating a set of measurements as a time series is being explored. Time Series Analysis (TSA) techniques, part of the Exploratory Data Analysis (EDA) approach, can provide much insight regarding the stochastic correlations that are induced on the outcome of an experiment by the measurement system and can provide criteria for the limited use of the classical variance in metrology. Specifically, techniques such as the Lag Plots, Autocorrelation Function, Power Spectral Density and Allan Variance are used to analyze series of sequential measurements, collected at equal time intervals from an electromechanical transducer. These techniques are used in conjunction with power law models of stochastic noise in order to characterize time or frequency regimes for which the usually assumed white noise model is adequate for the description of the measurement system response. However, through the detection of colored noise, usually referred to as flicker noise, which is expected to appear ...
Weighted statistical parameters for irregularly sampled time series
Rimoldini, Lorenzo
2014-01-01
Unevenly spaced time series are common in astronomy because of the day-night cycle, weather conditions, dependence on the source position in the sky, allocated telescope time, corrupt measurements, for example, or be inherent to the scanning law of satellites like Hipparcos and the forthcoming Gaia. This paper aims at improving the accuracy of common statistical parameters for the characterization of irregularly sampled signals. The uneven representation of time series, often including clumps of measurements and gaps with no data, can severely disrupt the values of estimators. A weighting scheme adapting to the sampling density and noise level of the signal is formulated. Its application to time series from the Hipparcos periodic catalogue led to significant improvements in the overall accuracy and precision of the estimators with respect to the unweighted counterparts and those weighted by inverse-squared uncertainties. Automated classification procedures employing statistical parameters weighted by the sugg...
A refined fuzzy time series model for stock market forecasting
Jilani, Tahseen Ahmed; Burney, Syed Muhammad Aqil
2008-05-01
Time series models have been used to make predictions of stock prices, academic enrollments, weather, road accident casualties, etc. In this paper we present a simple time-variant fuzzy time series forecasting method. The proposed method uses heuristic approach to define frequency-density-based partitions of the universe of discourse. We have proposed a fuzzy metric to use the frequency-density-based partitioning. The proposed fuzzy metric also uses a trend predictor to calculate the forecast. The new method is applied for forecasting TAIEX and enrollments’ forecasting of the University of Alabama. It is shown that the proposed method work with higher accuracy as compared to other fuzzy time series methods developed for forecasting TAIEX and enrollments of the University of Alabama.
Image-Based Learning Approach Applied to Time Series Forecasting
Directory of Open Access Journals (Sweden)
J. C. Chimal-Eguía
2012-06-01
Full Text Available In this paper, a new learning approach based on time-series image information is presented. In order to implementthis new learning technique, a novel time-series input data representation is also defined. This input datarepresentation is based on information obtained by image axis division into boxes. The difference between this newinput data representation and the classical is that this technique is not time-dependent. This new information isimplemented in the new Image-Based Learning Approach (IBLA and by means of a probabilistic mechanism thislearning technique is applied to the interesting problem of time series forecasting. The experimental results indicatethat by using the methodology proposed in this article, it is possible to obtain better results than with the classicaltechniques such as artificial neuronal networks and support vector machines.
Minimum entropy density method for the time series analysis
Lee, Jeong Won; Park, Joongwoo Brian; Jo, Hang-Hyun; Yang, Jae-Suk; Moon, Hie-Tae
2009-01-01
The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the pattern is revealed most. The MEDM is applied to the financial time series of Standard and Poor’s 500 index from February 1983 to April 2006. Then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis.
Periodicity Estimation in Mechanical Acoustic Time-Series Data
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Zhu Yongbo
2015-01-01
Full Text Available Periodicity estimation in mechanical acoustic time-series data is a well-established problem in data mining as it can be applicable in variety of disciplines either for anomaly detection or for prediction purposes in industry. In this paper, we develop a new approach for capturing and characterizing periodic patterns in time-series data by virtue of the dynamic time warping (DTW. We have conducted extensive experiments to evaluate the proposed approach with synthetic data and our collected data in practice. Experimental results demonstrated its effectiveness and robustness on periodicity detection in highly noised data.
Detecting structural breaks in time series via genetic algorithms
DEFF Research Database (Denmark)
Doerr, Benjamin; Fischer, Paul; Hilbert, Astrid
2016-01-01
Detecting structural breaks is an essential task for the statistical analysis of time series, for example, for fitting parametric models to it. In short, structural breaks are points in time at which the behaviour of the time series substantially changes. Typically, no solid background knowledge...... and mutation operations for this problem, we conduct extensive experiments to determine good choices for the parameters and operators of the genetic algorithm. One surprising observation is that use of uniform and one-point crossover together gave significantly better results than using either crossover...
A new look at sunspot formation using theory and observations
Losada, I. R.; Warnecke, J.; Glogowski, K.; Roth, M.; Brandenburg, A.; Kleeorin, N.; Rogachevskii, I.
2017-10-01
Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are the origin of the bipolar sunspot structure seen on the solar surface. However, this theory has been challenged, in particular recently by new surface observation, helioseismic inversions, and numerical models of convective dynamos. In this article we discuss another theoretical approach to the formation of sunspots: the negative effective magnetic pressure instability. This is a large-scale instability, in which the total (kinetic plus magnetic) turbulent pressure can be suppressed in the presence of a weak large-scale magnetic field, leading to a converging downflow, which eventually concentrates the magnetic field within it. Numerical simulations of forced stratified turbulence have been able to produce strong super-equipartition flux concentrations, similar to sunspots at the solar surface. In this framework, sunspots would only form close to the surface due to the instability constraints on stratification and rotation. Additionally, we present some ideas from local helioseismology, where we plan to use the Hankel analysis to study the pre-emergence phase of a sunspot and to constrain its deep structure and formation mechanism.
Time Series Analysis of Wheat Futures Reward in China
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Different from the fact that the main researches are focused on single futures contract and lack of the comparison of different periods, this paper described the statistical characteristics of wheat futures reward time series of Zhengzhou Commodity Exchange in recent three years. Besides the basic statistic analysis, the paper used the GARCH and EGARCH model to describe the time series which had the ARCH effect and analyzed the persistence of volatility shocks and the leverage effect. The results showed that compared with that of normal one,wheat futures reward series were abnormality, leptokurtic and thick tail distribution. The study also found that two-part of the reward series had no autocorrelation. Among the six correlative series, three ones presented the ARCH effect. By using of the Auto-regressive Distributed Lag Model, GARCH model and EGARCH model, the paper demonstrates the persistence of volatility shocks and the leverage effect on the wheat futures reward time series. The results reveal that on the one hand, the statistical characteristics of the wheat futures reward are similar to the aboard mature futures market as a whole. But on the other hand, the results reflect some shortages such as the immatureness and the over-control by the government in the Chinese future market.
The Application of Kernel Smoothing to Time Series Data
Institute of Scientific and Technical Information of China (English)
Zhao-jun Wang; Yi Zhao; Chun-jie Wu; Yan-ting Li
2006-01-01
There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data.Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn't work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package axe applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS's method.
Recurrent Neural Network Applications for Astronomical Time Series
Protopapas, Pavlos
2017-06-01
The benefits of good predictive models in astronomy lie in early event prediction systems and effective resource allocation. Current time series methods applicable to regular time series have not evolved to generalize for irregular time series. In this talk, I will describe two Recurrent Neural Network methods, Long Short-Term Memory (LSTM) and Echo State Networks (ESNs) for predicting irregular time series. Feature engineering along with a non-linear modeling proved to be an effective predictor. For noisy time series, the prediction is improved by training the network on error realizations using the error estimates from astronomical light curves. In addition to this, we propose a new neural network architecture to remove correlation from the residuals in order to improve prediction and compensate for the noisy data. Finally, I show how to set hyperparameters for a stable and performant solution correctly. In this work, we circumvent this obstacle by optimizing ESN hyperparameters using Bayesian optimization with Gaussian Process priors. This automates the tuning procedure, enabling users to employ the power of RNN without needing an in-depth understanding of the tuning procedure.
A Revised Collection of Sunspot Group Numbers
Vaquero, J M; Carrasco, V M S; Clette, F; Lefèvre, L; Gallego, M C; Arlt, R; Aparicio, A J P; Richard, J -G; Howe, R
2016-01-01
We describe a revised collection of the number of sunspot groups from 1610 to the present. This new collection is based on the work of Hoyt and Schatten (Solar Phys. 179, 189, 1998). The main changes are the elimination of a considerable number of observations during the Maunder Minimum (hereafter, MM) and the inclusion of several long series of observations. Numerous minor changes are also described. Moreover, we have calculated the active-day percentage during the MM from this new collection as a reliable index of the solar activity. Thus, the level of solar activity obtained in this work is greater than the level obtained using the original Hoyt and Schatten data, although it remains compatible with a grand minimum of solar activity. The new collection is available in digital format.
The sunspot cycle recorded in the thermoluminescence profile of the GT89/3 Ionian sea core
Energy Technology Data Exchange (ETDEWEB)
Cini Castagnoli, G.; Bonino, G.; Taricco, C. [Turin Univ. (Italy). Ist. di Fisica Generale]|[CNR, Turin (Italy). Ist. di Cosmogeofisica
1997-11-01
The authors measured the thermoluminescence (TL) depth of the GT89/3 shallow-water Ionian sea core. This profile has been transformed into a time series using the accurate sedimentation rate previously determined by radiometric and tephroanalysis methods. The TL measurements were performed in samples of equal thickness of 2 mm, corresponding to a time interval of 3.096 y. The TL time series spans {approx} 1800 y. The DFT power spectral densities in the decadal periodicity range of this TL series show significant periodicities at 10.7, 11.3 and 12 y closely similar to the periodicities present in the sunspot number series. These results confirm that the TL signal in recent sea sediments faithfully records the solar variability, as we previously proposed.
Time Series Analysis Based on Running Mann Whitney Z Statistics
A sensitive and objective time series analysis method based on the calculation of Mann Whitney U statistics is described. This method samples data rankings over moving time windows, converts those samples to Mann-Whitney U statistics, and then normalizes the U statistics to Z statistics using Monte-...
Nonlinear projective filtering; 1, Application to real time series
Schreiber, T
1998-01-01
We discuss applications of nonlinear filtering of time series by locally linear phase space projections. Noise can be reduced whenever the error due to the manifold approximation is smaller than the noise in the system. Examples include the real time extraction of the fetal electrocardiogram from abdominal recordings.
Sparse time series chain graphical models for reconstructing genetic networks
Abegaz, Fentaw; Wit, Ernst
2013-01-01
We propose a sparse high-dimensional time series chain graphical model for reconstructing genetic networks from gene expression data parametrized by a precision matrix and autoregressive coefficient matrix. We consider the time steps as blocks or chains. The proposed approach explores patterns of co
Optimization of recurrent neural networks for time series modeling
DEFF Research Database (Denmark)
Pedersen, Morten With
1997-01-01
The present thesis is about optimization of recurrent neural networks applied to time series modeling. In particular is considered fully recurrent networks working from only a single external input, one layer of nonlinear hidden units and a li near output unit applied to prediction of discrete time...
Mining approximate periodic pattern in hydrological time series
Zhu, Y. L.; Li, S. J.; Bao, N. N.; Wan, D. S.
2012-04-01
There is a lot of information about the hidden laws of nature evolution and the influences of human beings activities on the earth surface in long sequence of hydrological time series. Data mining technology can help find those hidden laws, such as flood frequency and abrupt change, which is useful for the decision support of hydrological prediction and flood control scheduling. The periodic nature of hydrological time series is important for trend forecasting of drought and flood and hydraulic engineering planning. In Hydrology, the full period analysis of hydrological time series has attracted a lot of attention, such as the discrete periodogram, simple partial wave method, Fourier analysis method, and maximum entropy spectral analysis method and wavelet analysis. In fact, the hydrological process is influenced both by deterministic factors and stochastic ones. For example, the tidal level is also affected by moon circling the Earth, in addition to the Earth revolution and its rotation. Hence, there is some kind of approximate period hidden in the hydrological time series, sometimes which is also called the cryptic period. Recently, partial period mining originated from the data mining domain can be a remedy for the traditional period analysis methods in hydrology, which has a loose request of the data integrity and continuity. They can find some partial period in the time series. This paper is focused on the partial period mining in the hydrological time series. Based on asynchronous periodic pattern and partial period mining with suffix tree, this paper proposes to mine multi-event asynchronous periodic pattern based on modified suffix tree representation and traversal, and invent a dynamic candidate period intervals adjusting method, which can avoids period omissions or waste of time and space. The experimental results on synthetic data and real water level data of the Yangtze River at Nanjing station indicate that this algorithm can discover hydrological
Real Time Clustering of Time Series Using Triangular Potentials
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Aldo Pacchiano
2015-01-01
Full Text Available Motivated by the problem of computing investment portfolio weightin gs we investigate various methods of clustering as alternatives to traditional mean-v ariance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets w hich share similar return characteristics over time and treat each group as a singl e composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present as sociated theoretical results as well as various examples based on synthetic data.
A Platform for Processing Expression of Short Time Series (PESTS
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Markatou Marianthi
2011-01-01
Full Text Available Abstract Background Time course microarray profiles examine the expression of genes over a time domain. They are necessary in order to determine the complete set of genes that are dynamically expressed under given conditions, and to determine the interaction between these genes. Because of cost and resource issues, most time series datasets contain less than 9 points and there are few tools available geared towards the analysis of this type of data. Results To this end, we introduce a platform for Processing Expression of Short Time Series (PESTS. It was designed with a focus on usability and interpretability of analyses for the researcher. As such, it implements several standard techniques for comparability as well as visualization functions. However, it is designed specifically for the unique methods we have developed for significance analysis, multiple test correction and clustering of short time series data. The central tenet of these methods is the use of biologically relevant features for analysis. Features summarize short gene expression profiles, inherently incorporate dependence across time, and allow for both full description of the examined curve and missing data points. Conclusions PESTS is fully generalizable to other types of time series analyses. PESTS implements novel methods as well as several standard techniques for comparability and visualization functions. These features and functionality make PESTS a valuable resource for a researcher's toolkit. PESTS is available to download for free to academic and non-profit users at http://www.mailman.columbia.edu/academic-departments/biostatistics/research-service/software-development.
Time Series Outlier Detection Based on Sliding Window Prediction
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Yufeng Yu
2014-01-01
Full Text Available In order to detect outliers in hydrological time series data for improving data quality and decision-making quality related to design, operation, and management of water resources, this research develops a time series outlier detection method for hydrologic data that can be used to identify data that deviate from historical patterns. The method first built a forecasting model on the history data and then used it to predict future values. Anomalies are assumed to take place if the observed values fall outside a given prediction confidence interval (PCI, which can be calculated by the predicted value and confidence coefficient. The use of PCI as threshold is mainly on the fact that it considers the uncertainty in the data series parameters in the forecasting model to address the suitable threshold selection problem. The method performs fast, incremental evaluation of data as it becomes available, scales to large quantities of data, and requires no preclassification of anomalies. Experiments with different hydrologic real-world time series showed that the proposed methods are fast and correctly identify abnormal data and can be used for hydrologic time series analysis.
Sunspot waves and flare energy release
Sych, R; Altyntsev, A; Dudík, J; Kashapova, L
2014-01-01
We address a possibility of the flare process initiation and further maintenance of its energy release due to a transformation of sunspot longitudinal waves into transverse magnetic loop oscillations with initiation of reconnection. This leads to heating maintaining after the energy release peak and formation of a flat stage on the X-ray profile. We applied the time-distance plots and pixel wavelet filtration (PWF) methods to obtain spatio-temporal distribution of wave power variations in SDO/AIA data. To find magnetic waveguides, we used magnetic field extrapolation of SDO/HMI magnetograms. The propagation velocity of wave fronts was measured from their spatial locations at specific times. In correlation curves of the 17 GHz (NoRH) radio emission we found a monotonous energy amplification of 3-min waves in the sunspot umbra before the 2012 June 7 flare. This dynamics agrees with an increase in the wave-train length in coronal loops (SDO/AIA, 171 {\\AA}) reaching the maximum 30 minutes prior to the flare onset...
Time series hyperspectral chemical imaging data: challenges, solutions and applications.
Gowen, A A; Marini, F; Esquerre, C; O'Donnell, C; Downey, G; Burger, J
2011-10-31
Hyperspectral chemical imaging (HCI) integrates imaging and spectroscopy resulting in three-dimensional data structures, hypercubes, with two spatial and one wavelength dimension. Each spatial image pixel in a hypercube contains a spectrum with >100 datapoints. While HCI facilitates enhanced monitoring of multi-component systems; time series HCI offers the possibility of a more comprehensive understanding of the dynamics of such systems and processes. This implies a need for modeling strategies that can cope with the large multivariate data structures generated in time series HCI experiments. The challenges posed by such data include dimensionality reduction, temporal morphological variation of samples and instrumental drift. This article presents potential solutions to these challenges, including multiway analysis, object tracking, multivariate curve resolution and non-linear regression. Several real world examples of time series HCI data are presented to illustrate the proposed solutions. Copyright © 2011 Elsevier B.V. All rights reserved.
Complex Network Approach to the Fractional Time Series
Manshour, Pouya
2015-01-01
In order to extract the correlation information inherited in a stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map the fractional processes onto complex networks. The parabolic exponential functions are found to ?fit with the corresponding degree distributions, with Hurst dependent ?fitting parameter. Further, we take into account other topological properties such as the maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for the antipersistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between the node's degree and its corresp...
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
Extracting unstable periodic orbits from chaotic time series data
Energy Technology Data Exchange (ETDEWEB)
So, P.; Schiff, S.; Gluckman, B.J., [Center for Neuroscience, Childrens Research Institute, Childrens National Medical Center and the George Washington University, NW, Washington, D.C. 20010 (United States); So, P.; Ott, E.; Grebogi, C., [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Sauer, T., [Department of Mathematics, The George Mason University, Fairfax, Virginia 22030 (United States); Gluckman, B.J., [Naval Surface Warfare Center, Carderock Division, Bethesda, Maryland 20054-5000 (United States)
1997-05-01
A general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed. By utilizing the estimated local dynamics along a trajectory, we devise a transformation of the time series data such that the transformed data are concentrated on the periodic orbits. Thus, one can extract unstable periodic orbits from a chaotic time series by simply looking for peaks in a finite grid approximation of the distribution function of the transformed data. Our method is demonstrated using data from both numerical and experimental examples, including neuronal ensemble data from mammalian brain slices. The statistical significance of the results in the presence of noise is assessed using surrogate data. {copyright} {ital 1997} {ital The American Physical Society}
Parameter-Free Search of Time-Series Discord
Institute of Scientific and Technical Information of China (English)
Wei Luo; Marcus Gallagher; Janet Wiles
2013-01-01
Time-series discord is widely used in data mining applications to characterize anomalous subsequences in time series.Compared to some other discord search algorithms,the direct search algorithm based on the recurrence plot shows the advantage of being fast and parameter free.The direct search algorithm,however,relies on quasi-periodicity in input time series,an assumption that limits the algorithm's applicability.In this paper,we eliminate the periodicity assumption from the direct search algorithm by proposing a reference function for subsequences and a new sampling strategy based on the reference function.These measures result in a new algorithm with improved efficiency and robustness,as evidenced by our empirical evaluation.
GAS DETECTING AND FORECASTING VIA TIME SERIES METHOD
Institute of Scientific and Technical Information of China (English)
黄养光
1990-01-01
The importance and urgency of gas detecting and forecasting in underground coal mining are self-evident. Unfortunately, this problem has not yet been solved thoroughly. In this paper, the author suggests that the time series analysis method be adopted for processing the gas stochastic data. The time series method is superior to the conventional Fourier analysis in some aspects, especially, the time series method possesses Forecasting (or prediction) function which is highly valuable for gas monitoring. An example ot a set ot gas data sampled From a certain foul coal mine is investigated and an AR (3) model is established. The fitting result and the forecasting error are accepted satisfactorily. At the end of this paper several remarks are presented for further discussion.
The time series forecasting: from the aspect of network
Chen, S; Hu, Y; Liu, Q; Deng, Y
2014-01-01
Forecasting can estimate the statement of events according to the historical data and it is considerably important in many disciplines. At present, time series models have been utilized to solve forecasting problems in various domains. In general, researchers use curve fitting and parameter estimation methods (moment estimation, maximum likelihood estimation and least square method) to forecast. In this paper, a new sight is given to the forecasting and a completely different method is proposed to forecast time series. Inspired by the visibility graph and link prediction, this letter converts time series into network and then finds the nodes which are mostly likelihood to link with the predicted node. Finally, the predicted value will be obtained according to the state of the link. The TAIEX data set is used in the case study to illustrate that the proposed method is effectiveness. Compared with ARIMA model, the proposed shows a good forecasting performance when there is a small amount of data.
Feature-preserving interpolation and filtering of environmental time series
Mariethoz, Gregoire; Jougnot, Damien; Rezaee, Hassan
2015-01-01
We propose a method for filling gaps and removing interferences in time series for applications involving continuous monitoring of environmental variables. The approach is non-parametric and based on an iterative pattern-matching between the affected and the valid parts of the time series. It considers several variables jointly in the pattern matching process and allows preserving linear or non-linear dependences between variables. The uncertainty in the reconstructed time series is quantified through multiple realizations. The method is tested on self-potential data that are affected by strong interferences as well as data gaps, and the results show that our approach allows reproducing the spectral features of the original signal. Even in the presence of intense signal perturbations, it significantly improves the signal and corrects bias introduced by asymmetrical interferences. Potential applications are wide-ranging, including geophysics, meteorology and hydrology.
Causal analysis of time series from hydrological systems
Selle, Benny; Aufgebauer, Britta; Knorr, Klaus-Holger
2017-04-01
It is often difficult to infer cause and effect in hydrological systems for which time series of system inputs, outputs and state variables are observed. A recently published technique called Convergent Cross Mapping could be a promising tool to detect causality between time series. A response variable Y may be causally related to a forcing variable X, if the so called cross mapping of X using Y improves with the amount of data included. The idea is that a response variable contains information on the history of its driving variable whereas the reverse may not be true. We propose an alternative approach based on similar ideas using neural networks. Our approach is firstly compared to Convergent Cross Mapping using a synthetic time series of precipitation and streamflow generated by a rainfall runoff model. Secondly, measured concentrations of dissolved organic carbon and dissolved iron from a mountainous stream in Germany, that were previously hypothesised to be casually linked, are tested.
On the detection of superdiffusive behaviour in time series
Gottwald, G. A.; Melbourne, I.
2016-12-01
We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data (with no prior knowledge required of the nature of the data) and relies on one realisation (ie one sample path) of the process. Linear drift effects are automatically removed without any preprocessing. We show numerical results for time series constructed from i.i.d. α-stable random variables and from deterministic weakly chaotic maps. We compare our method with the standard method of estimating the growth rate of the mean-square displacement as well as the p-variation method, maximum likelihood, quantile matching and linear regression of the empirical characteristic function.
Increment entropy as a measure of complexity for time series
Liu, Xiaofeng; Xu, Ning; Xue, Jianru
2015-01-01
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters, one letter corresponding to direction and the other corresponding to magnitude. The Shannon entropy of the words is termed as increment entropy (IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have demonstrated its ability of detecting the abrupt change, regardless of energetic (e.g. spikes or bursts) or structural changes. The computation of IncrEn does not make any assumption on time series and it can be applicable to arbitrary real-world data.
Grammar-based feature generation for time-series prediction
De Silva, Anthony Mihirana
2015-01-01
This book proposes a novel approach for time-series prediction using machine learning techniques with automatic feature generation. Application of machine learning techniques to predict time-series continues to attract considerable attention due to the difficulty of the prediction problems compounded by the non-linear and non-stationary nature of the real world time-series. The performance of machine learning techniques, among other things, depends on suitable engineering of features. This book proposes a systematic way for generating suitable features using context-free grammar. A number of feature selection criteria are investigated and a hybrid feature generation and selection algorithm using grammatical evolution is proposed. The book contains graphical illustrations to explain the feature generation process. The proposed approaches are demonstrated by predicting the closing price of major stock market indices, peak electricity load and net hourly foreign exchange client trade volume. The proposed method ...
Time Series Prediction based on Hybrid Neural Networks
Directory of Open Access Journals (Sweden)
S. A. Yarushev
2016-01-01
Full Text Available In this paper, we suggest to use hybrid approach to time series forecasting problem. In first part of paper, we create a literature review of time series forecasting methods based on hybrid neural networks and neuro-fuzzy approaches. Hybrid neural networks especially effective for specific types of applications such as forecasting or classification problem, in contrast to traditional monolithic neural networks. These classes of problems include problems with different characteristics in different modules. The main part of paper create a detailed overview of hybrid networks benefits, its architectures and performance under traditional neural networks. Hybrid neural networks models for time series forecasting are discussed in the paper. Experiments with modular neural networks are given.
Time series, correlation matrices and random matrix models
Energy Technology Data Exchange (ETDEWEB)
Vinayak [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca (Mexico); Seligman, Thomas H. [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México and Centro Internacional de Ciencias, C.P. 62210 Cuernavaca (Mexico)
2014-01-08
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.
Track Irregularity Time Series Analysis and Trend Forecasting
Directory of Open Access Journals (Sweden)
Jia Chaolong
2012-01-01
Full Text Available The combination of linear and nonlinear methods is widely used in the prediction of time series data. This paper analyzes track irregularity time series data by using gray incidence degree models and methods of data transformation, trying to find the connotative relationship between the time series data. In this paper, GM (1,1 is based on first-order, single variable linear differential equations; after an adaptive improvement and error correction, it is used to predict the long-term changing trend of track irregularity at a fixed measuring point; the stochastic linear AR, Kalman filtering model, and artificial neural network model are applied to predict the short-term changing trend of track irregularity at unit section. Both long-term and short-term changes prove that the model is effective and can achieve the expected accuracy.
Increment Entropy as a Measure of Complexity for Time Series
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Xiaofeng Liu
2016-01-01
Full Text Available Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce an increment entropy to measure the complexity of time series in which each increment is mapped onto a word of two letters, one corresponding to the sign and the other corresponding to the magnitude. Increment entropy (IncrEn is defined as the Shannon entropy of the words. Simulations on synthetic data and tests on epileptic electroencephalogram (EEG signals demonstrate its ability of detecting abrupt changes, regardless of the energetic (e.g., spikes or bursts or structural changes. The computation of IncrEn does not make any assumption on time series, and it can be applicable to arbitrary real-world data.
Time series characterization via horizontal visibility graph and Information Theory
Gonçalves, Bruna Amin; Carpi, Laura; Rosso, Osvaldo A.; Ravetti, Martín G.
2016-12-01
Complex networks theory have gained wider applicability since methods for transformation of time series to networks were proposed and successfully tested. In the last few years, horizontal visibility graph has become a popular method due to its simplicity and good results when applied to natural and artificially generated data. In this work, we explore different ways of extracting information from the network constructed from the horizontal visibility graph and evaluated by Information Theory quantifiers. Most works use the degree distribution of the network, however, we found alternative probability distributions, more efficient than the degree distribution in characterizing dynamical systems. In particular, we find that, when using distributions based on distances and amplitude values, significant shorter time series are required. We analyze fractional Brownian motion time series, and a paleoclimatic proxy record of ENSO from the Pallcacocha Lake to study dynamical changes during the Holocene.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Neural network versus classical time series forecasting models
Nor, Maria Elena; Safuan, Hamizah Mohd; Shab, Noorzehan Fazahiyah Md; Asrul, Mohd; Abdullah, Affendi; Mohamad, Nurul Asmaa Izzati; Lee, Muhammad Hisyam
2017-05-01
Artificial neural network (ANN) has advantage in time series forecasting as it has potential to solve complex forecasting problems. This is because ANN is data driven approach which able to be trained to map past values of a time series. In this study the forecast performance between neural network and classical time series forecasting method namely seasonal autoregressive integrated moving average models was being compared by utilizing gold price data. Moreover, the effect of different data preprocessing on the forecast performance of neural network being examined. The forecast accuracy was evaluated using mean absolute deviation, root mean square error and mean absolute percentage error. It was found that ANN produced the most accurate forecast when Box-Cox transformation was used as data preprocessing.
Appropriate Algorithms for Nonlinear Time Series Analysis in Psychology
Scheier, Christian; Tschacher, Wolfgang
Chaos theory has a strong appeal for psychology because it allows for the investigation of the dynamics and nonlinearity of psychological systems. Consequently, chaos-theoretic concepts and methods have recently gained increasing attention among psychologists and positive claims for chaos have been published in nearly every field of psychology. Less attention, however, has been paid to the appropriateness of chaos-theoretic algorithms for psychological time series. An appropriate algorithm can deal with short, noisy data sets and yields `objective' results. In the present paper it is argued that most of the classical nonlinear techniques don't satisfy these constraints and thus are not appropriate for psychological data. A methodological approach is introduced that is based on nonlinear forecasting and the method of surrogate data. In artificial data sets and empirical time series we can show that this methodology reliably assesses nonlinearity and chaos in time series even if they are short and contaminated by noise.
A multidisciplinary database for geophysical time series management
Montalto, P.; Aliotta, M.; Cassisi, C.; Prestifilippo, M.; Cannata, A.
2013-12-01
The variables collected by a sensor network constitute a heterogeneous data source that needs to be properly organized in order to be used in research and geophysical monitoring. With the time series term we refer to a set of observations of a given phenomenon acquired sequentially in time. When the time intervals are equally spaced one speaks of period or sampling frequency. Our work describes in detail a possible methodology for storage and management of time series using a specific data structure. We designed a framework, hereinafter called TSDSystem (Time Series Database System), in order to acquire time series from different data sources and standardize them within a relational database. The operation of standardization provides the ability to perform operations, such as query and visualization, of many measures synchronizing them using a common time scale. The proposed architecture follows a multiple layer paradigm (Loaders layer, Database layer and Business Logic layer). Each layer is specialized in performing particular operations for the reorganization and archiving of data from different sources such as ASCII, Excel, ODBC (Open DataBase Connectivity), file accessible from the Internet (web pages, XML). In particular, the loader layer performs a security check of the working status of each running software through an heartbeat system, in order to automate the discovery of acquisition issues and other warning conditions. Although our system has to manage huge amounts of data, performance is guaranteed by using a smart partitioning table strategy, that keeps balanced the percentage of data stored in each database table. TSDSystem also contains modules for the visualization of acquired data, that provide the possibility to query different time series on a specified time range, or follow the realtime signal acquisition, according to a data access policy from the users.
Sunspot Observations of Rudolf Wolf from 1849 - 1893
Friedli, Thomas K.
2016-06-01
The sunspot observations of Rudolf Wolf form the core of the Wolf series of sunspot relative numbers, or Wolf numbers, since his observations define the original scale of the series and also the main course of solar activity from 1849 to 1893. Unfortunately, the raw data for the years 1856 to 1869 were never published in full detail. The heritage group of the Rudolf Wolf Society in Switzerland digitized parts of the hitherto unpublished original source book of the Wolf series and put it on its website www.wolfinstitute.ch. Now, the Wolf numbers from 1849 to 1876, as provided by the World Data Center for Solar Index and Long-term Solar Observations (WDC-SILSO), can be reconstructed in every detail, since the source book contains all the raw sunspot group and individual spot numbers as well as the implemented calibration and interpolation methods. Thus, the observations made by Rudolf Wolf with the 83/1320 mm Fraunhofer refractor and with the 40/700 mm Parisian refractor as well as those made by Heinrich Schwabe can be identified and separated now. In this article, we describe Wolf's instruments and methods of observation. An inspection of the source book and other published sources reveals that the calibration factor of the 40/700 mm Parisian refractor should probably be lowered. Since no appropriate comparison observations are available, the scale transfer from Heinrich Schwabe to Rudolf Wolf has to be analyzed further.
Does Building a Relative Sunspot Number Make Sense? A Qualified 'Yes'
Svalgaard, Leif
2015-01-01
Recent research has demonstrated that the number of sunspots per group ('active region') has been decreasing over the last two or three solar cycles and that the classical Relative Sunspot Number (SSN) no longer is a good representation of solar magnetic activity such as revealed by e.g. the F10.7 cm microwave flux. The SSN is derived under the assumption that the number of spots per group is constant (in fact, nominally equal to 10). When this is no longer the case (the ratio is approaching 5, only half of its nominal value) the question arises how to construct a sunspot number series that takes that into account. We propose to harmonize the SSN with the sunspot Group Count that has been shown to follow F10.7 very well, but also to include the day-to-day variations of the spot count in order to preserve both long-term and short-term variability.
A novel time series link prediction method: Learning automata approach
Moradabadi, Behnaz; Meybodi, Mohammad Reza
2017-09-01
Link prediction is a main social network challenge that uses the network structure to predict future links. The common link prediction approaches to predict hidden links use a static graph representation where a snapshot of the network is analyzed to find hidden or future links. For example, similarity metric based link predictions are a common traditional approach that calculates the similarity metric for each non-connected link and sort the links based on their similarity metrics and label the links with higher similarity scores as the future links. Because people activities in social networks are dynamic and uncertainty, and the structure of the networks changes over time, using deterministic graphs for modeling and analysis of the social network may not be appropriate. In the time-series link prediction problem, the time series link occurrences are used to predict the future links In this paper, we propose a new time series link prediction based on learning automata. In the proposed algorithm for each link that must be predicted there is one learning automaton and each learning automaton tries to predict the existence or non-existence of the corresponding link. To predict the link occurrence in time T, there is a chain consists of stages 1 through T - 1 and the learning automaton passes from these stages to learn the existence or non-existence of the corresponding link. Our preliminary link prediction experiments with co-authorship and email networks have provided satisfactory results when time series link occurrences are considered.
Detection of "noisy" chaos in a time series
DEFF Research Database (Denmark)
Chon, K H; Kanters, J K; Cohen, R J
1997-01-01
, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations...... the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series...
A Non-standard Empirical Likelihood for Time Series
DEFF Research Database (Denmark)
Nordman, Daniel J.; Bunzel, Helle; Lahiri, Soumendra N.
Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version......-standard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi...
Dominant Skyline Query Processing over Multiple Time Series
Institute of Scientific and Technical Information of China (English)
Hao Wang; Chao-Kun Wang; Ya-Jun Xu; Yuan-Chi Ning
2013-01-01
Multiple time series (MTS),which describes an object in multi-dimensions,is based on single time series and has been proved to be useful.In this paper,a new analytical method called α/β-Dominant-Skyline on MTS and a formal definition of the α/β-dominant skyline MTS are given.Also,three algorithms,called NL,BC and MFB,are proposed to address the α/β-dominant skyline queries over MTS.Finally experimental results on both synthetic and real data verify the correctness and effectiveness of the proposed method and algorithms.
Testing for intracycle determinism in pseudoperiodic time series
Coelho, Mara C. S.; Mendes, Eduardo M. A. M.; Aguirre, Luis A.
2008-06-01
A determinism test is proposed based on the well-known method of the surrogate data. Assuming predictability to be a signature of determinism, the proposed method checks for intracycle (e.g., short-term) determinism in the pseudoperiodic time series for which standard methods of surrogate analysis do not apply. The approach presented is composed of two steps. First, the data are preprocessed to reduce the effects of seasonal and trend components. Second, standard tests of surrogate analysis can then be used. The determinism test is applied to simulated and experimental pseudoperiodic time series and the results show the applicability of the proposed test.
Mining Rules from Electrical Load Time Series Data Set
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The mining of the rules from the electrical load time series data which are collected from the EMS (Energy Management System) is discussed. The data from the EMS are too huge and sophisticated to be understood and used by the power system engineer, while useful information is hidden in the electrical load data. The authors discuss the use of fuzzy linguistic summary as data mining method to induce the rules from the electrical load time series. The data preprocessing techniques are also discussed in the paper.
Nonlinear Time Series Forecast Using Radial Basis Function Neural Networks
Institute of Scientific and Technical Information of China (English)
ZHENGXin; CHENTian-Lun
2003-01-01
In the research of using Radial Basis Function Neural Network (RBF NN) forecasting nonlinear time series, we investigate how the different clusterings affect the process of learning and forecasting. We find that k-means clustering is very suitable. In order to increase the precision we introduce a nonlinear feedback term to escape from the local minima of energy, then we use the model to forecast the nonlinear time series which are produced by Mackey-Glass equation and stocks. By selecting the k-means clustering and the suitable feedback term, much better forecasting results are obtained.
Bootstrap Power of Time Series Goodness of fit tests
Directory of Open Access Journals (Sweden)
Sohail Chand
2013-10-01
Full Text Available In this article, we looked at power of various versions of Box and Pierce statistic and Cramer von Mises test. An extensive simulation study has been conducted to compare the power of these tests. Algorithms have been provided for the power calculations and comparison has also been made between the semi parametric bootstrap methods used for time series. Results show that Box-Pierce statistic and its various versions have good power against linear time series models but poor power against non linear models while situation reverses for Cramer von Mises test. Moreover, we found that dynamic bootstrap method is better than xed design bootstrap method.
Complex network approach for recurrence analysis of time series
Energy Technology Data Exchange (ETDEWEB)
Marwan, Norbert, E-mail: marwan@pik-potsdam.d [Potsdam Institute for Climate Impact Research, PO Box 601203, 14412 Potsdam (Germany); Donges, Jonathan F. [Potsdam Institute for Climate Impact Research, PO Box 601203, 14412 Potsdam (Germany)] [Department of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin (Germany); Zou Yong [Potsdam Institute for Climate Impact Research, PO Box 601203, 14412 Potsdam (Germany); Donner, Reik V. [Potsdam Institute for Climate Impact Research, PO Box 601203, 14412 Potsdam (Germany)] [Institute for Transport and Economics, Dresden University of Technology, Andreas-Schubert-Str. 23, 01062 Dresden (Germany)] [Graduate School of Science, Osaka Prefecture University, 1-1 Gakuencho, Naka-ku, Sakai 599-8531 (Japan); Kurths, Juergen [Potsdam Institute for Climate Impact Research, PO Box 601203, 14412 Potsdam (Germany)] [Department of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin (Germany)
2009-11-09
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
Chaotic time series prediction and additive white Gaussian noise
Energy Technology Data Exchange (ETDEWEB)
Lim, Teck Por [Department of Mathematics, 6M30 Huxley, Imperial College London, 180 Queen' s Gate, London, SW7 2BZ (United Kingdom)]. E-mail: teckpor@gmail.com; Puthusserypady, Sadasivan [Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576 (Singapore)]. E-mail: elespk@nus.edu.sg
2007-06-04
Taken's delay embedding theorem states that a pseudo state-space can be reconstructed from a time series consisting of observations of a chaotic process. However, experimental observations are inevitably corrupted by measurement noise, which can be modelled as Additive White Gaussian Noise (AWGN). This Letter analyses time series prediction in the presence of AWGN using the triangle inequality and the mean of the Nakagami distribution. It is shown that using more delay coordinates than those used by a typical delay embedding can improve prediction accuracy, when the mean magnitude of the input vector dominates the mean magnitude of AWGN.
Parameterizing unconditional skewness in models for financial time series
DEFF Research Database (Denmark)
He, Changli; Silvennoinen, Annastiina; Teräsvirta, Timo
In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate...... unconditional skewness. We consider modelling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional...
Handbook of Time Series Analysis Recent Theoretical Developments and Applications
Schelter, Björn; Timmer, Jens
2006-01-01
This handbook provides an up-to-date survey of current research topics and applications of time series analysis methods written by leading experts in their fields. It covers recent developments in univariate as well as bivariate and multivariate time series analysis techniques ranging from physics' to life sciences' applications. Each chapter comprises both methodological aspects and applications to real world complex systems, such as the human brain or Earth's climate. Covering an exceptionally broad spectrum of topics, beginners, experts and practitioners who seek to understand the latest de
Microbial oceanography and the Hawaii Ocean Time-series programme.
Karl, David M; Church, Matthew J
2014-10-01
The Hawaii Ocean Time-series (HOT) programme has been tracking microbial and biogeochemical processes in the North Pacific Subtropical Gyre since October 1988. The near-monthly time series observations have revealed previously undocumented phenomena within a temporally dynamic ecosystem that is vulnerable to climate change. Novel microorganisms, genes and unexpected metabolic pathways have been discovered and are being integrated into our evolving ecological paradigms. Continued research, including higher-frequency observations and at-sea experimentation, will help to provide a comprehensive scientific understanding of microbial processes in the largest biome on Earth.
Kālī: Time series data modeler
Kasliwal, Vishal P.
2016-07-01
The fully parallelized and vectorized software package Kālī models time series data using various stochastic processes such as continuous-time ARMA (C-ARMA) processes and uses Bayesian Markov Chain Monte-Carlo (MCMC) for inferencing a stochastic light curve. Kālimacr; is written in c++ with Python language bindings for ease of use. K¯lī is named jointly after the Hindu goddess of time, change, and power and also as an acronym for KArma LIbrary.
Chromospheric seismology above sunspot umbrae
Snow, B; Regnier, S
2015-01-01
The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected. In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed. The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours---white, pink and brown---as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line of sight (LOS) integration is also performed to determine the observable spectra through SDO/AIA. The numerical results show that the gradient of the coronal ...
A window-based time series feature extraction method.
Katircioglu-Öztürk, Deniz; Güvenir, H Altay; Ravens, Ursula; Baykal, Nazife
2017-08-09
This study proposes a robust similarity score-based time series feature extraction method that is termed as Window-based Time series Feature ExtraCtion (WTC). Specifically, WTC generates domain-interpretable results and involves significantly low computational complexity thereby rendering itself useful for densely sampled and populated time series datasets. In this study, WTC is applied to a proprietary action potential (AP) time series dataset on human cardiomyocytes and three precordial leads from a publicly available electrocardiogram (ECG) dataset. This is followed by comparing WTC in terms of predictive accuracy and computational complexity with shapelet transform and fast shapelet transform (which constitutes an accelerated variant of the shapelet transform). The results indicate that WTC achieves a slightly higher classification performance with significantly lower execution time when compared to its shapelet-based alternatives. With respect to its interpretable features, WTC has a potential to enable medical experts to explore definitive common trends in novel datasets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fractal dimension of electroencephalographic time series and underlying brain processes.
Lutzenberger, W; Preissl, H; Pulvermüller, F
1995-10-01
Fractal dimension has been proposed as a useful measure for the characterization of electrophysiological time series. This paper investigates what the pointwise dimension of electroencephalographic (EEG) time series can reveal about underlying neuronal generators. The following theoretical assumptions concerning brain function were made (i) within the cortex, strongly coupled neural assemblies exist which oscillate at certain frequencies when they are active, (ii) several such assemblies can oscillate at a time, and (iii) activity flow between assemblies is minimal. If these assumptions are made, cortical activity can be considered as the weighted sum of a finite number of oscillations (plus noise). It is shown that the correlation dimension of finite time series generated by multiple oscillators increases monotonically with the number of oscillators. Furthermore, it is shown that a reliable estimate of the pointwise dimension of the raw EEG signal can be calculated from a time series as short as a few seconds. These results indicate that (i) The pointwise dimension of the EEG allows conclusions regarding the number of independently oscillating networks in the cortex, and (ii) a reliable estimate of the pointwise dimension of the EEG is possible on the basis of short raw signals.
FTSPlot: fast time series visualization for large datasets.
Riss, Michael
2014-01-01
The analysis of electrophysiological recordings often involves visual inspection of time series data to locate specific experiment epochs, mask artifacts, and verify the results of signal processing steps, such as filtering or spike detection. Long-term experiments with continuous data acquisition generate large amounts of data. Rapid browsing through these massive datasets poses a challenge to conventional data plotting software because the plotting time increases proportionately to the increase in the volume of data. This paper presents FTSPlot, which is a visualization concept for large-scale time series datasets using techniques from the field of high performance computer graphics, such as hierarchic level of detail and out-of-core data handling. In a preprocessing step, time series data, event, and interval annotations are converted into an optimized data format, which then permits fast, interactive visualization. The preprocessing step has a computational complexity of O(n x log(N)); the visualization itself can be done with a complexity of O(1) and is therefore independent of the amount of data. A demonstration prototype has been implemented and benchmarks show that the technology is capable of displaying large amounts of time series data, event, and interval annotations lag-free with visualization method for long-term electrophysiological experiments.
Short dynamic fibrils in sunspot chromospheres
van der Voort, Luc Rouppe
2013-01-01
Sunspot chromospheres display vigorous oscillatory signature when observed in chromospheric diagnostics like the strong Ca II lines and H-alpha. New high-resolution sunspot observations from the Swedish 1-m Solar Telescope show the ubiquitous presence of small-scale periodic jet-like features that move up and down. This phenomenon has not been described before. Their typical width is about 0.3 arcsec and they display clear parabolic trajectories in space-time diagrams. The maximum extension of the top of the jets is lowest in the umbra, a few 100 km, and progressively longer further away from the umbra in the penumbra, with the longest more than 1000 km. These jets resemble dynamic fibrils found in plage regions but at smaller extensions. LTE inversion of spectro-polarimetric Ca II 8542 observations enabled for a comparison of the magnetic field inclination and the properties of these short jets. We find that the most extended of these jets also have longer periods and tend to be located in regions with more ...
Power computations in time series analyses for traffic safety interventions.
McLeod, A Ian; Vingilis, E R
2008-05-01
The evaluation of traffic safety interventions or other policies that can affect road safety often requires the collection of administrative time series data, such as monthly motor vehicle collision data that may be difficult and/or expensive to collect. Furthermore, since policy decisions may be based on the results found from the intervention analysis of the policy, it is important to ensure that the statistical tests have enough power, that is, that we have collected enough time series data both before and after the intervention so that a meaningful change in the series will likely be detected. In this short paper, we present a simple methodology for doing this. It is expected that the methodology presented will be useful for sample size determination in a wide variety of traffic safety intervention analysis applications. Our method is illustrated with a proposed traffic safety study that was funded by NIH.
LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES
Institute of Scientific and Technical Information of China (English)
Wei GAO; Zheng TIAN
2009-01-01
An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.
Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations
Scargle, Jeffrey D; Jackson, Brad; Chiang, James
2012-01-01
This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it - an improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of vari...
Recovery of delay time from time series based on the nearest neighbor method
Energy Technology Data Exchange (ETDEWEB)
Prokhorov, M.D., E-mail: mdprokhorov@yandex.ru [Saratov Branch of Kotel' nikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019 (Russian Federation); Ponomarenko, V.I. [Saratov Branch of Kotel' nikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov 410019 (Russian Federation); Department of Nano- and Biomedical Technologies, Saratov State University, Astrakhanskaya Street, 83, Saratov 410012 (Russian Federation); Khorev, V.S. [Department of Nano- and Biomedical Technologies, Saratov State University, Astrakhanskaya Street, 83, Saratov 410012 (Russian Federation)
2013-12-09
We propose a method for the recovery of delay time from time series of time-delay systems. The method is based on the nearest neighbor analysis. The method allows one to reconstruct delays in various classes of time-delay systems including systems of high order, systems with several coexisting delays, and nonscalar time-delay systems. It can be applied to time series heavily corrupted by additive and dynamical noise.
Recovery of delay time from time series based on the nearest neighbor method
Prokhorov, M. D.; Ponomarenko, V. I.; Khorev, V. S.
2013-12-01
We propose a method for the recovery of delay time from time series of time-delay systems. The method is based on the nearest neighbor analysis. The method allows one to reconstruct delays in various classes of time-delay systems including systems of high order, systems with several coexisting delays, and nonscalar time-delay systems. It can be applied to time series heavily corrupted by additive and dynamical noise.
A Data Mining Framework for Time Series Estimation
Hu, Xiao; Xu, Peng; Wu, Shaozhi; Asgari, Shadnaz; Bergsneider, Marvin
2009-01-01
Time series estimation techniques are usually employed in biomedical research to derive variables less accessible from a set of related and more accessible variables. These techniques are traditionally built from systems modeling approaches including simulation, blind decovolution, and state estimation. In this work, we define target time series (TTS) and its related time series (RTS) as the output and input of a time series estimation process, respectively. We then propose a novel data mining framework for time series estimation when TTS and RTS represent different sets of observed variables from the same dynamic system. This is made possible by mining a database of instances of TTS, its simultaneously recorded RTS, and the input/output dynamic models between them. The key mining strategy is to formulate a mapping function for each TTS-RTS pair in the database that translates a feature vector extracted from RTS to the dissimilarity between true TTS and its estimate from the dynamic model associated with the same TTS-RTS pair. At run time, a feature vector is extracted from an inquiry RTS and supplied to the mapping function associated with each TTS-RTS pair to calculate a dissimilarity measure. An optimal TTS-RTS pair is then selected by analyzing these dissimilarity measures. The associated input/output model of the selected TTS-RTS pair is then used to simulate the TTS given the inquiry RTS as an input. An exemplary implementation was built to address a biomedical problem of noninvasive intracranial pressure assessment. The performance of the proposed method was superior to that of a simple training-free approach of finding the optimal TTS-RTS pair by a conventional similarity-based search on RTS features. PMID:19900575
Change detection in a time series of polarimetric SAR images
DEFF Research Database (Denmark)
Skriver, Henning; Nielsen, Allan Aasbjerg; Conradsen, Knut
can be used to detect at which points changes occur in the time series. [1] T. W. Anderson, An Introduction to Multivariate Statistical Analysis, John Wiley, New York, third edition, 2003. [2] K. Conradsen, A. A. Nielsen, J. Schou, and H. Skriver, “A test statistic in the complex Wishart distribution...
Deriving dynamic marketing effectiveness from econometric time series models
C. Horváth (Csilla); Ph.H.B.F. Franses (Philip Hans)
2003-01-01
textabstractTo understand the relevance of marketing efforts, it has become standard practice to estimate the long-run and short-run effects of the marketing-mix, using, say, weekly scanner data. A common vehicle for this purpose is an econometric time series model. Issues that are addressed in the
United States forest disturbance trends observed with landsat time series
Jeffrey G. Masek; Samuel N. Goward; Robert E. Kennedy; Warren B. Cohen; Gretchen G. Moisen; Karen Schleweiss; Chengquan. Huang
2013-01-01
Disturbance events strongly affect the composition, structure, and function of forest ecosystems; however, existing US land management inventories were not designed to monitor disturbance. To begin addressing this gap, the North American Forest Dynamics (NAFD) project has examined a geographic sample of 50 Landsat satellite image time series to assess trends in forest...
Real Rainfall Time Series for Storm Sewer Design
DEFF Research Database (Denmark)
Larsen, Torben
1981-01-01
This paper describes a simulation method for the design of retention storages, overflows etc. in storm sewer systems. The method is based on computer simulation with real real rainfall time series as input and with a simple transfer model of the ARMA-type (Autoregressive moving average) applied...
Real Rainfall Time Series for Storm Sewer Design
DEFF Research Database (Denmark)
Larsen, Torben
The paper describes a simulation method for the design of retention storages, overflows etc. in storm sewer systems. The method is based on computer simulation with real rainfall time series as input ans with the aply of a simple transfer model of the ARMA-type (autoregressiv moving average model...
Daily time series evapotranspiration maps for Oklahoma and Texas panhandle
Evapotranspiration (ET) is an important process in ecosystems’ water budget and closely linked to its productivity. Therefore, regional scale daily time series ET maps developed at high and medium resolutions have large utility in studying the carbon-energy-water nexus and managing water resources. ...
Analysis of Complex Intervention Effects in Time-Series Experiments.
Bower, Cathleen
An iterative least squares procedure for analyzing the effect of various kinds of intervention in time-series data is described. There are numerous applications of this design in economics, education, and psychology, although until recently, no appropriate analysis techniques had been developed to deal with the model adequately. This paper…
Noise in multivariate GPS position time-series
Amiri-Simkooei, A.R.
2008-01-01
A methodology is developed to analyze a multivariate linear model, which occurs in many geodetic and geophysical applications. Proper analysis of multivariate GPS coordinate time-series is considered to be an application. General, special, and more practical stochastic models are adopted to assess t
Application of modern time series analysis to high stability oscillators
Farrell, B. F.; Mattison, W. M.; Vessot, R. F. C.
1980-01-01
Techniques of modern time series analysis useful for investigating the characteristics of high-stability oscillators and identifying systematic perturbations are discussed with reference to an experiment in which the frequencies of superconducting cavity-stabilized oscillators and hydrogen masers were compared. The techniques examined include transformation to stationarity, autocorrelation and cross-correlation, superresolution, and transfer function determination.
Long-memory time series theory and methods
Palma, Wilfredo
2007-01-01
Wilfredo Palma, PhD, is Chairman and Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. Dr. Palma has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics.
Wavelet methods in (financial) time-series processing
Struzik, Z.R.
2000-01-01
We briefly describe the major advantages of using the wavelet transform for the processing of financial time series on the example of the S&P index. In particular, we show how to uncover local the scaling (correlation) characteristics of the S&P index with the wavelet based effective H'older expone
Noise in multivariate GPS position time-series
Amiri-Simkooei, A.R.
2008-01-01
A methodology is developed to analyze a multivariate linear model, which occurs in many geodetic and geophysical applications. Proper analysis of multivariate GPS coordinate time-series is considered to be an application. General, special, and more practical stochastic models are adopted to assess t