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.
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.
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.
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
Time Series Prediction Based on Chaotic Attractor
Institute of Scientific and Technical Information of China (English)
LIKe-Ping; CHENTian-Lun; GAOZi-You
2003-01-01
A new prediction technique is proposed for chaotic time series. The usefulness of the technique is that it can kick off some false neighbor points which are not suitable for the local estimation of the dynamics systems. A time-delayed embedding is used to reconstruct the underlying attractor, and the prediction model is based on the time evolution of the topological neighboring in the phase space. We use a feedforward neural network to approximate the local dominant Lyapunov exponent, and choose the spatial neighbors by the Lyapunov exponent. The model is tested for the Mackey-Glass equation and the convection amplitude of lorenz systems. The results indicate that this prediction technique can improve the prediction of chaotic time series.
Application of a Local Polynomial Approximation Chaotic Time Series Prediction
Orzeszko, Witold
2004-01-01
Chaos theory has become a new approach to financial processes analysis. Due to complicated dynamics, chaotic time series seem to be random and, in consequence, unpredictable. In fact, unlike truly random processes, chaotic dynamics can be forecasted very precisely in a short run. In this paper, a local polynomial approximation is presented. Its efficiency, as a method of building short-term predictors of chaotic time series, has been examined. The presented method has been applied to forecast...
Chaotic time series prediction using artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
Bartlett, E.B.
1991-01-01
This paper describes the use of artificial neural networks to model the complex oscillations defined by a chaotic Verhuist animal population dynamic. A predictive artificial neural network model is developed and tested, and results of computer simulations are given. These results show that the artificial neural network model predicts the chaotic time series with various initial conditions, growth parameters, or noise.
Chaotic time series prediction using artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
Bartlett, E.B.
1991-12-31
This paper describes the use of artificial neural networks to model the complex oscillations defined by a chaotic Verhuist animal population dynamic. A predictive artificial neural network model is developed and tested, and results of computer simulations are given. These results show that the artificial neural network model predicts the chaotic time series with various initial conditions, growth parameters, or noise.
A data-fitting procedure for chaotic time series
Energy Technology Data Exchange (ETDEWEB)
McDonough, J.M.; Mukerji, S. [Univ. of Kentucky, Lexington, KY (United States). Dept. of Mechanical Engineering; Chung, S. [Univ. of Illinois, Urbana, IL (United States)
1998-10-01
In this paper the authors introduce data characterizations for fitting chaotic data to linear combinations of one-dimensional maps (say, of the unit interval) for use in subgrid-scale turbulence models. They test the efficacy of these characterizations on data generated by a chaotically-forced Burgers` equation and demonstrate very satisfactory results in terms of modeled time series, power spectra and delay maps.
A Novel Adaptive Predictor for Chaotic Time Series
Institute of Scientific and Technical Information of China (English)
BU Yun; WEN Guang-Jun; ZHOU Xiao-Jia; ZHANG Qiang
2009-01-01
Many chaotic time series show non-Gaussian distribution, and non-Gaussianity can be characterized not only by higher-order cumulants but also by negative entropy.Since negative entropy can be accurately approximated by some special non-polynomial functions, which also can form an orthogonal system, these functions are used to construct an adaptive predictor to replace higher-order cumulants.Simulation shows the algorithm performs well for different chaotic systems.
Chaotic time series. Part II. System Identification and Prediction
Directory of Open Access Journals (Sweden)
Bjørn Lillekjendlie
1994-10-01
Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.
Chaotic time series analysis in economics: Balance and perspectives
International Nuclear Information System (INIS)
The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area
Chaotic time series analysis in economics: Balance and perspectives
Energy Technology Data Exchange (ETDEWEB)
Faggini, Marisa, E-mail: mfaggini@unisa.it [Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Fisciano 84084 (Italy)
2014-12-15
The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.
PREDICTING CHAOTIC TIME SERIES WITH IMPROVED LOCAL APPROXIMATIONS
Institute of Scientific and Technical Information of China (English)
MU Xiaowu; LIN Lan; ZHOU Xiangdong
2004-01-01
In this paper, new approaches for chaotic time series prediction are introduced.We first summarize and evaluate the existing local prediction models, then propose optimization models and new algorithms to modify procedures of local approximations. The modification to the choice of sample sets is given, and the zeroth-order approximation is improved by a linear programming method. Four procedures of first-order approximation are compared, and corresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predicting accuracy is put forward. In the end, we discuss two important examples, i.e. Lorenz system and Rossler system, and the simulation experiments indicate that the modified algorithms are effective.
The improved local linear prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
Meng Qing-Fang; Peng Yu-Hua; Sun Jia
2007-01-01
Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time aeries. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time aeries and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.
Local discrete cosine transformation domain Volterra prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
张家树; 李恒超; 肖先赐
2005-01-01
In this paper a local discrete cosine transformation (DCT) domain Volterra prediction method is proposed to predict chaotic time series, where the DCT is used to lessen the complexity of solving the coefficient matrix. Numerical simulation results show that the proposed prediction method can effectively predict chaotic time series and improve the prediction accuracy compared with the traditional local linear prediction methods.
PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL
Institute of Scientific and Technical Information of China (English)
MA Jun-hai; WANG Zhi-qiang; CHEN Yu-shu
2006-01-01
The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques, but also discusses prediction techniques of chaotic time series and its applications based on chaotic data noise reduction. In the paper, we first decompose the phase space of chaotic time series to range space and null noise space. Secondly we restructure original chaotic time series in range space. Lastly on the basis of the above, we establish order of the nonlinear model and make use of the nonlinear model to predict some research. The result indicates that the nonlinear modelhas very strong ability of approximation function, and Chaos predict method has certain tutorial significance to the practical problems.
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
International Nuclear Information System (INIS)
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated. (general)
Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter
Zhang, Jia-Shu; Xiao, Xian-Ci
2001-03-01
A newly proposed method, i.e. the adaptive higher-order nonlinear finite impulse response (HONFIR) filter based on higher-order sparse Volterra series expansions, is introduced to predict hyper-chaotic time series. The effectiveness of using the adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including the Mackey-Glass equation and four-dimensional nonlinear dynamical system. A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series. Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
Prediction of chaotic time series based on modified minimax probability machine regression
Institute of Scientific and Technical Information of China (English)
Sun Jian-Cheng
2007-01-01
Long-term prediction of chaotic time series is very difficult, for the chaos restricts predictability. In thie paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression (MPMR). Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error (MSE) and absolute error (AE) as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.
Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network
International Nuclear Information System (INIS)
This paper proposes a co-evolutionary recurrent neural network (CERNN) for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by co-evolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets: the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series
Chaotic Characteristic of Time Series of Partial Discharge in Oil-Paper Insulation
International Nuclear Information System (INIS)
The chaotic characteristics of time series of five partial discharge (PD) patterns in oil-paper insulation are studied. The results verify obvious chaotic characteristic of the time series of discharge signals and the fact that PD is a chaotic process. These time series have distinctive features, and the chaotic attractors obtained from time series differed greatly from each other by shapes in the phase space, so they could be used to qualitatively identify the PD patterns. The phase space parameters are selected, then the chaotic characteristic quantities can be extracted. These quantities could quantificationally characterize the PD patterns. The effects on pattern recognition of PRPD and CAPD are compared by using the neural network of radial basis function. The results show that both of the two recognition methods work well and have their respective advantages. Then, both the statistical operators under PRPD mode and the chaotic characteristic quantities under CAPD mode are selected comprehensively as the input vectors of neural network, and the PD pattern recognition accuracy is thereby greatly improved. (15th asian conference on electrical discharge)
Prediction and analysis of chaotic time series on the basis of support vector
Institute of Scientific and Technical Information of China (English)
Li Tianliang; He Liming; Li Haipeng
2008-01-01
Based on discussion on the theories of support vector machines(SVM),an one-step prediction model for time series prediction is presented,wherein the chaos theory is incorporated.Chaotic character of the time series is taken into account in the prediction procedure;parameters of reconstruction-delay and embedding-dimension for phase-space reconstruction are calculated in light of mutual-information and false-nearest-neighbor method,respectively.Precision and functionality have been demonstrated by the experimental results on the basis of the prediction of Lorenz chaotic time series.
Mackey-Glass noisy chaotic time series prediction by a swarm-optimized neural network
López-Caraballo, C. H.; Salfate, I.; Lazzús, J. A.; Rojas, P.; Rivera, M.; Palma-Chilla, L.
2016-05-01
In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass noiseless chaotic time series in the short-term and long-term prediction. The performance prediction is evaluated and compared with similar work in the literature, particularly for the long-term forecast. Also, we present properties of the dynamical system via the study of chaotic behaviour obtained from the time series prediction. Then, this standard hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions that also allowed us compute uncertainties of predictions for noisy Mackey-Glass chaotic time series. We study the impact of noise for three cases with a white noise level (σ N ) contribution of 0.01, 0.05 and 0.1.
Institute of Scientific and Technical Information of China (English)
柳景青; 张士乔; 俞申凯
2004-01-01
The chaotic characteristics and maximum predictable time scale of the observation series of hourly water consumption in Hangzhou were investigated using the advanced algorithm presented here is based on the conventional Wolf's algorithm for the largest Lyapunov exponent. For comparison, the largest Lyapunov exponents of water consumption series with one-hour and 24-hour intervals were calculated respectively. The results indicated that chaotic characteristics obviously exist in the hourly water consumption system; and that observation series with 24-hour interval have longer maximum predictable scale than hourly series. These findings could have significant practical application for better prediction of urban hourly water consumption.
Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series
Directory of Open Access Journals (Sweden)
Qing Li
2016-01-01
Full Text Available According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO. The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA and BP neural network (BPNN model in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.
New prediction of chaotic time series based on local Lyapunov exponent
International Nuclear Information System (INIS)
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. (general)
Time series cross prediction in a single transistor chaotic circuit using neural networks
Directory of Open Access Journals (Sweden)
L. Magafas
2009-01-01
Full Text Available In this paper we will be trying to cross predict a multivariate time series of a single transistor chaotic circuit using neural networks. For this purpose we investigate the influence of a number of first and second order near neighbors in predicting chaotic time series using a back propagation neural network. This influence is examined by changing the number of neurons in the hidden layer of a backprogation neural network with one hidden layer. The number of neurons at the input layer were equal to the embedding dimension of the corresponding strange attractor.
International Nuclear Information System (INIS)
This paper introduces a novel algorithm for determining the structure of a radial basis function (RBF) network (the number of hidden units) while it is used for dynamic modeling of chaotic time series. It can be seen that the hidden units in the RBF network can form hyperplanes to partition the input space into various regions in each of which it is possible to approximate the dynamics with a basis function. The number of regions corresponds to the number of hidden units. The basic idea of the proposed algorithm is to partition the input space by fractal scaling of the chaotic time series being modeled. By fractal scaling process, the number of basis functions (hidden units) as well as the number of input variables can be specified. Accordingly, the network topology is efficiently determined based on the complexity of the underlying dynamics as reflected in the observed time series. The feasibility of the proposed scheme is examined through dynamic modeling of the well-known chaotic time series. The results show that the new method can improve the predictability of chaotic time series with a suitable number of hidden units compared to that of reported in the literature
Multi-Scale Gaussian Processes: a Novel Model for Chaotic Time Series Prediction
Institute of Scientific and Technical Information of China (English)
ZHOU Ya-Tong; ZHANG Tai-Yi; SUN Jian-Cheng
2007-01-01
@@ Based on the classical Gaussian process (GP) model, we propose a multi-scale Gaussian process (MGP) model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
Chaotic time series prediction using mean-field theory for support vector machine
Institute of Scientific and Technical Information of China (English)
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Directory of Open Access Journals (Sweden)
Jun Wang
2015-01-01
Full Text Available The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.
Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series
Directory of Open Access Journals (Sweden)
Liu Hai
2015-01-01
Full Text Available Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.
Modelling of chaotic time series using a variable-length windowing approach
International Nuclear Information System (INIS)
A multidimensional feature extraction method for chaotic time series is presented. The method uses a variable-length windowing approach. Mackey-Glass delay-difference equation is used to create chaotic sample signals. Among many possible alternatives, the length of the data segment having the smallest variance fractal dimension (VFD) value is found and used as the feature value. Multidimensional feature vectors are formed to model each sample signal. A probabilistic neural network (PNN) is trained and tested with these vectors. It is shown that the application of the new feature extraction method improves the classification performance of the PNN as compared to a VFD based feature extraction method using a fix-length windowing approach
The Application of Direction Basis Function Neural Networks to the Prediction of Chaotic Time Series
Institute of Scientific and Technical Information of China (English)
CAOWenming
2004-01-01
In this paper we have examined the ability of Direction basis function networks (DBFN) to predict the output of a chaotic time series generated from a model of a physical system. DBFNs are known to be universal approximators, and chaotic systems are known to exhibit “random” behavior. Therefore the challenge is to apply the DBFN to the prediction of the output of a chaotic system, which we have chosen here to be the Mackey-Glass delay differential equation. The DBFN has been trained with off-line supervised learning using a Recursive Least Squares optimization for obtaining weights. Key issues which are addressed are the estimation of the order of the system and dependence of prediction error on various factors such as placement of DBF centers, selection of perceptive widths, and number of training samples. Included in this study is an implementation of Moody and Darken's K Means Clustering approach to optimally place DBF centers and a heuristic nearest neighbor method for determining perceptive widths.
Future mission studies: Forecasting solar flux directly from its chaotic time series
Ashrafi, S.
1991-01-01
The mathematical structure of the programs written to construct a nonlinear predictive model to forecast solar flux directly from its time series without reference to any underlying solar physics is presented. This method and the programs are written so that one could apply the same technique to forecast other chaotic time series, such as geomagnetic data, attitude and orbit data, and even financial indexes and stock market data. Perhaps the most important application of this technique to flight dynamics is to model Goddard Trajectory Determination System (GTDS) output of residues between observed position of spacecraft and calculated position with no drag (drag flag = off). This would result in a new model of drag working directly from observed data.
Shen, Meie; Chen, Wei-Neng; Zhang, Jun; Chung, Henry Shu-Hung; Kaynak, Okyay
2013-04-01
The optimal selection of parameters for time-delay embedding is crucial to the analysis and the forecasting of chaotic time series. Although various parameter selection techniques have been developed for conventional uniform embedding methods, the study of parameter selection for nonuniform embedding is progressed at a slow pace. In nonuniform embedding, which enables different dimensions to have different time delays, the selection of time delays for different dimensions presents a difficult optimization problem with combinatorial explosion. To solve this problem efficiently, this paper proposes an ant colony optimization (ACO) approach. Taking advantage of the characteristic of incremental solution construction of the ACO, the proposed ACO for nonuniform embedding (ACO-NE) divides the solution construction procedure into two phases, i.e., selection of embedding dimension and selection of time delays. In this way, both the embedding dimension and the time delays can be optimized, along with the search process of the algorithm. To accelerate search speed, we extract useful information from the original time series to define heuristics to guide the search direction of ants. Three geometry- or model-based criteria are used to test the performance of the algorithm. The optimal embeddings found by the algorithm are also applied in time-series forecasting. Experimental results show that the ACO-NE is able to yield good embedding solutions from both the viewpoints of optimization performance and prediction accuracy. PMID:23144038
Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression
Institute of Scientific and Technical Information of China (English)
YE Mei-Ying; WANG Xiao-Dong
2005-01-01
A new class of support vector machine, nu-support vector machine, is discussed which can handle both classification and regression. We focus on nu-support vector machine regression and use it for phase space prediction of compares nu-support vector machine with back propagation (BP) networks in order to better evaluate the performance of the proposed methods. The experimental results show that the nu-support vector machine regression obtains lower root mean squared error than the BP networks and provides an accurate chaotic time series prediction. These results can be attributable to the fact that nu-support vector machine implements the structural risk minimization principle and this leads to better generalization than the BP networks.
Research on Optimize Prediction Model and Algorithm about Chaotic Time Series
Institute of Scientific and Technical Information of China (English)
JIANG Wei-jin; XU Yu-sheng
2004-01-01
We put forward a chaotic estimating model.by using the parameter of the chaotic system, sensitivity of the parameter to inching and control the disturbance of the system, and estimated the parameter of the model by using the best update option.In the end, we forecast the intending series value in its mutually space.The example shows that it can increase the precision in the estimated process by selecting the best model steps.It not only conquer the abuse of using detention inlay technology alone, but also decrease blindness of using forecast error to decide the input model directly, and the result of it is better than the method of statistics and other series means.
International Nuclear Information System (INIS)
An iterative optimization method is used to uncover unobserved initial state (t = 0), historical evolutionary path (t 0) and parameters of a chaotic process from a segment of scalar time series (t0 ≤ t ≤ t1, t0 > 0). Given the system structure, we can precisely estimate the model parameters, recover the trajectory components unobserved, identify the state of all variables at the beginning (t = t0) of the observed time series, and trace the historical evolution of the system back to a long time interval (0 ≤ t 0). Chaotic time series of Lorenz system and Roessler system are utilized for illustration. The results show that the method is effective and tolerant to large mismatches between the guessed and actual values of the initial state and parameters
International Nuclear Information System (INIS)
A finite impulse response neural network, with tap delay lines after each neuron in hidden layer, is used. Genetic algorithm with arithmetic decimal crossover and Roulette selection with normal probability mutation method with linear combination rule is used for optimization of FIR neural network. The method is applied for prediction of several important and benchmarks chaotic time series such as: geomagnetic activity index natural time series and famous Mackey-Glass time series. The results of simulations shows that applying dynamic neural models for modeling of highly nonlinear chaotic systems is more satisfactory with respect to feed forward neural networks. Likewise, global optimization method such as genetic algorithm is more efficient in comparison of nonlinear gradient based optimization methods like momentum term, conjugate gradient.
A method to improve the precision of chaotic time series prediction by using a non-trajectory
Institute of Scientific and Technical Information of China (English)
Yan Hua; Wei Ping; Xiao Xian-Ci
2009-01-01
Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems,the error of chaotic time series prediction increases with the prediction step.This paper provides a method to improve the prediction precision by adjusting the predicted value in the course of iteration according to the evolution information of small intervals on the Lett and right sides of the predicted value.The adjusted predicted result is a non-trajectory which can provide a better prediction performance than the usual result based on the trajectory.Numerical simulations of two typical chaotic maps demonstrate its effectiveness.When the prediction step gets relatively larger,the effect is more pronounced.
A method to improve the precision of chaotic time series prediction by using a non-trajectory
International Nuclear Information System (INIS)
Due to the error in the measured value of the initial state and the sensitive dependence on initial conditions of chaotic dynamical systems, the error of chaotic time series prediction increases with the prediction step. This paper provides a method to improve the prediction precision by adjusting the predicted value in the course of iteration according to the evolution information of small intervals on the left and right sides of the predicted value. The adjusted predicted result is a non-trajectory which can provide a better prediction performance than the usual result based on the trajectory. Numerical simulations of two typical chaotic maps demonstrate its effectiveness. When the prediction step gets relatively larger, the effect is more pronounced. (general)
Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia
2016-01-01
Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field. PMID:27118260
Xu, Xijin; Tang, Qian; Xia, Haiyue; Zhang, Yuling; Li, Weiqiu; Huo, Xia
2016-04-01
Chaotic time series prediction based on nonlinear systems showed a superior performance in prediction field. We studied prenatal exposure to polychlorinated biphenyls (PCBs) by chaotic time series prediction using the least squares self-exciting threshold autoregressive (SEATR) model in umbilical cord blood in an electronic waste (e-waste) contaminated area. The specific prediction steps basing on the proposal methods for prenatal PCB exposure were put forward, and the proposed scheme’s validity was further verified by numerical simulation experiments. Experiment results show: 1) seven kinds of PCB congeners negatively correlate with five different indices for birth status: newborn weight, height, gestational age, Apgar score and anogenital distance; 2) prenatal PCB exposed group at greater risks compared to the reference group; 3) PCBs increasingly accumulated with time in newborns; and 4) the possibility of newborns suffering from related diseases in the future was greater. The desirable numerical simulation experiments results demonstrated the feasibility of applying mathematical model in the environmental toxicology field.
International Nuclear Information System (INIS)
Highlights: • Impact of meteorological factors on wind speed forecasting is taken into account. • Forecasted wind speed results are corrected by the associated rules. • Forecasting accuracy is improved by the new wind speed forecasting strategy. • Robust of the proposed model is validated by data sampled from different sites. - Abstract: Wind energy has been the fastest growing renewable energy resource in recent years. Because of the intermittent nature of wind, wind power is a fluctuating source of electrical energy. Therefore, to minimize the impact of wind power on the electrical grid, accurate and reliable wind power forecasting is mandatory. In this paper, a new wind speed forecasting approach based on based on the chaotic time series modelling technique and the Apriori algorithm has been developed. The new approach consists of four procedures: (I) Clustering by using the k-means clustering approach; (II) Employing the Apriori algorithm to discover the association rules; (III) Forecasting the wind speed according to the chaotic time series forecasting model; and (IV) Correcting the forecasted wind speed data using the associated rules discovered previously. This procedure has been verified by 31-day-ahead daily average wind speed forecasting case studies, which employed the wind speed and other meteorological data collected from four meteorological stations located in the Hexi Corridor area of China. The results of these case studies reveal that the chaotic forecasting model can efficiently improve the accuracy of the wind speed forecasting, and the Apriori algorithm can effectively discover the association rules between the wind speed and other meteorological factors. In addition, the correction results demonstrate that the association rules discovered by the Apriori algorithm have powerful capacities in handling the forecasted wind speed values correction when the forecasted values do not match the classification discovered by the association rules
Detection of chaotic determinism in time series from randomly forced maps
DEFF Research Database (Denmark)
Chon, K H; Kanters, J K; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos...... in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, 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...... 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, and applied to heart rate variability data....
Prediction of Gas Emission Based on Information Fusion and Chaotic Time Series
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In order to make more exact predictions of gas emissions, information fusion and chaos time series are combined to predict the amount of gas emission in pits. First, a multi-sensor information fusion frame is established. The frame includes a data level, a character level and a decision level. Functions at every level are interpreted in detail in this paper. Then, the process of information fusion for gas emission is introduced. On the basis of those data processed at the data and character levels, the chaos time series and neural network are combined to predict the amount of gas emission at the decision level. The weights of the neural network are gained by training not by manual setting, in order to avoid subjectivity introduced by human intervention. Finally, the experimental results were analyzed in Matlab 6.0 and prove that the method is more accurate in the prediction of the amount of gas emission than the traditional method.
Fathian Baneh, A.; Sarkhosh, L.
2013-12-01
Before August 11th, 2012 Arasbaran twin earthquakes (Mw 6.4 and Mw 6.3), no seismogenic fault has been fully recognized within the meizoseismal area of the events, neither there were obvious evidence on the microseismicity pattern of the region showing potentials of such activities for an earthquake to occur. In the present study, we tried to investigate the seismic activity of the area in a time period between 2006 and 2012 to verify whether symptoms are detectable in the seismicity of the region or not. In this case, we profited from two different approaches: a statistical method (considering which as a linear system) and Chaos theory (considering it as a non-linear system). We analyzed firstly the seismic time series based on magnitude/number of earthquakes versus time, using ARIMA modeling which refutes the linear behavior of the system. Therefore, we discussed the nonlinear behavior of earthquake time series of the study area to simply explain the complexities in the system using chaos theory for a time interval of six years. Moreover, the calculation of Lyapunov exponent was put into practice. Although results derived from ARIMA modeling indicate non-stability of the studied system and reveal the system undergoes a non-periodicity behavior, yet the positive estimated Lyapunov exponent obviously denotes the chaotic dynamics in the system. Such results could be used as a marker for more detailed further surveys of the areas which seem safe in terms of seismic hazard, as Arasbaran area was once deemed.
Gaussian小波SVM及其混沌时间序列预测%Gaussian Wavelet SVM and Its Applications to Chaotic Time Series Forecasting
Institute of Scientific and Technical Information of China (English)
郑永康; 陈维荣; 戴朝华; 王维博
2009-01-01
To improve the accuracy of chaotic time series forecasting,Gaussiun wavelet support vector machine (SVM) forecasting model is proposed,which combines the wavelet technology with SVM kernel function method,and based on that the wavelet is beneficial to extracting imperceptible features of signal.It is proved that the even order derivative Ganssian wavelet function is an admissible translation-invariant kernel of SVM,and corresponding Ganssian wavelet SVM is constructed.The chaotic time series is reconstructed in phase space,and the vector in phase space reconstruction is used as the input of SVM.The experiments of forecasting Chen's chaotic time series and load chaotic time series are conducted using the proposed SVM,the conventional radial basis SVM and the Morlet wavelet SVM respectively.The comparison results show that Gaussian wavelet SVM has better performance than the other two SVMs.%为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型.证明了偶数阶Ganssian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM.时混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量.用Ganssian小波SVM与常用的径向基SVM及Morlet小渡SVM进行对比实验,通过对Chen's混沌时间序列和负荷混沌时间序列的预测,结果表明,Ganssian小波SVM的效果比其他两种SVM更好.
Vaughan, Adam; Bohac, Stanislav V
2015-10-01
Fuel efficient Homogeneous Charge Compression Ignition (HCCI) engine combustion timing predictions must contend with non-linear chemistry, non-linear physics, period doubling bifurcation(s), turbulent mixing, model parameters that can drift day-to-day, and air-fuel mixture state information that cannot typically be resolved on a cycle-to-cycle basis, especially during transients. In previous work, an abstract cycle-to-cycle mapping function coupled with ϵ-Support Vector Regression was shown to predict experimentally observed cycle-to-cycle combustion timing over a wide range of engine conditions, despite some of the aforementioned difficulties. The main limitation of the previous approach was that a partially acasual randomly sampled training dataset was used to train proof of concept offline predictions. The objective of this paper is to address this limitation by proposing a new online adaptive Extreme Learning Machine (ELM) extension named Weighted Ring-ELM. This extension enables fully causal combustion timing predictions at randomly chosen engine set points, and is shown to achieve results that are as good as or better than the previous offline method. The broader objective of this approach is to enable a new class of real-time model predictive control strategies for high variability HCCI and, ultimately, to bring HCCI's low engine-out NOx and reduced CO2 emissions to production engines. PMID:26164437
International Nuclear Information System (INIS)
The Levenberg-Marquardt learning algorithm is applied for training a multilayer perception with three hidden layer each with ten neurons in order to carefully map the structure of chaotic time series such as Mackey-Glass time series. First the MLP network is trained with 1000 data, and then it is tested with next 500 data. After that the trained and tested network is applied for long-term prediction of next 120 data which come after test data. The prediction is such a way that, the first inputs to network for prediction are the four last data of test data, then the predicted value is shifted to the regression vector which is the input to the network, then after first four-step of prediction, the input regression vector to network is fully predicted values and in continue, each predicted data is shifted to input vector for subsequent prediction.
Institute of Scientific and Technical Information of China (English)
Xiang Yuanpeng; Cao Biao; Zeng Min; Huang Shisheng; Shao Lanjuan
2008-01-01
The experimental time series of welding current produced by carbon dioxide gas metal arc welding with shortcircuiting transfer were recorded and subsequently evaluated. Based on phase space reconstruction, the correlation dimensions and Kolmogorov entropies of the corresponding system have been numerically calculated using the Grassberger-Procaccia algorithm at different time delays. It was found out that the time delay has little effect on the estimation of correlation dimension; conversely,it plays a key role in producing precise results on the estimation of Kolmogorov entropy.
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system. PMID:25019866
Behavioural analysis of a time series–A chaotic approach
Indian Academy of Sciences (India)
T A Fathima; V Jothiprakash
2014-06-01
Out of the various methods available to study the chaotic behaviour, correlation dimension method (CDM) derived from Grassberger-Procaccia algorithm and False Nearest Neighbour method (FNN) are widely used. It is aimed to study the adaptability of those techniques for Indian rainfall data that is dominated by monsoon. In the present study, five sets of time series data are analyzed using correlation dimension method (CDM) based upon Grassberger-Procaccia algorithm for studying their behaviour. In order to confirm the results arrived from correlation dimension method, FNN and phase randomisation method is also applied to the time series used in the present study to fix the optimum embedding dimension. First series is a deterministic natural number series, the next two series are random number series with two types of distributions; one is uniform and another is normal distributed random number series. The fourth series is Henon data, an erratic data generated from a deterministic non linear equation (classified as chaotic series). After checking the applicability of correlation dimension method for deterministic, stochastic and chaotic data (known series) the method is applied to a rainfall time series observed at Koyna station, Maharashtra, India for its behavioural study. The results obtained from the chaotic analysis revealed that CDM is an efficient method for behavioural study of a time series. It also provides first hand information on the number of dimensions to be considered for time series prediction modelling. The CDM applied to real life rainfall data brings out the nature of rainfall at Koyna station as chaotic. For the rainfall data, CDM resulted in a minimum correlation dimension of one and optimum dimension as five. FNN method also resulted in five dimensions for the rainfall data. The behaviour of the rainfall time series is further confirmed by phase randomisation technique also. The surrogate data derived from randomisation gives entirely different
Chaotic time series prediction based on wavelet echo state network%基于小波回声状态网络的混沌时间序列预测
Institute of Scientific and Technical Information of China (English)
宋彤; 李菡
2012-01-01
混沌现象普遍存在于自然界及人类社会中，因此混沌时间序列预测具有重要意义．提出了一种新的混沌时间序列预测模型—小波回声状态网络，该模型可以有效克服传统回声状态网络模型中普遍存在的病态矩阵问题，提高了混沌时间序列预测精度．通过对Lorenz、含噪声Lorenz及间歇式反应釜釜温三个时间序列的预测，将小波回声状态网络与传统回声状态网络进行了比较．结果表明，小波回声状态网络与传统回声状态网络相比，预测精度提高一倍以上且预测结果更加稳定．%Chaos is widespread in nature and human society, so the prediction of chaotic time series is very important. In this paper, we propose a new chaotic time series prediction model - echo state network based on wavelet, which can effectively overcome the ill-posed problem that exists in traditional echo state networks. And it also has a good generalization ability. Three time series are used to test the new model, i.e., Lorenz time series, Lorenz time series with added noise and batch reactor vessel temperature time series. Results suggest that the new proposed method can achieve a higher predictable accuracy, better generalization and more stable prediction results than traditional echo state networks.
Directory of Open Access Journals (Sweden)
Matías Rafti
2010-01-01
Full Text Available Se estudia la influencia del procedimiento de filtrado aplicado sobre series temporales para su uso en la caracterización y detección de regímenes no-lineales. Para esto, se toma como ejemplo de dichos métodos, un algoritmo ampliamente utilizado para el cálculo de la dimensión de correlación de la trayectoria en el espacio de las fases (el algoritmo de Grassberger-Procaccia. El interés de este ejemplo de estudio radica en la similitud con el procedimiento que se aplica al analizar imágenes experimentales de sistemas fisicoquímicos de reacción-difusión, provenientes de técnicas de análisis superficial como la microscopía de emisión de fotoelectrones. Los resultados de las simulaciones realizadas muestran como el uso de un parámetro de filtrado inadecuado puede conducir a caracterizar erróneamente estados como no lineales o caóticos.The influence of the filtering scheme on time series for their use in the characterization and detection of non lineal regimes. As an example, the Grassberger-Procaccia algorithm for phase-space trajectory correlation dimension is used The main interest of such analysis is to study the similarities with the processing of experimental images from reaction-diffusion systems obtained via surface science standard tools such as photoelectron emission microscopy. Simulation results show how inadequate filtering parameter choice may lead to erroneous characterization of systems as non-linear or chaotic.
Synchronization of complex chaotic systems in series expansion form
International Nuclear Information System (INIS)
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Synchronization of complex chaotic systems in series expansion form
Energy Technology Data Exchange (ETDEWEB)
Ge Zhengming [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)]. E-mail: zmg@cc.nctu.edu.tw; Yang Chenghsiung [Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan (China)
2007-12-15
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy.
多元混沌时间序列的相关状态机预测模型研究%Research on Multivariate Chaotic Time Series Prediction Using mRSM Model
Institute of Scientific and Technical Information of China (English)
韩敏; 许美玲; 任伟杰
2014-01-01
Considering that there may be overfitting problem, as well as the problem of high dimensional redundant input variables in multivariate chaotic time series prediction, we introduce a novel multivariate prediction model based on relevance vector machine and echo state network, named multivariate relevance state machine (mRSM). The proposed model reconstructs the multivariate chaotic time series into the phase space, then reduces the dimension of input variables with the principal component analysis method. Subsequently, the mRSM uses a reservoir, replacing kernel functions of relevance vector machine, to map the dynamic features of multivariate time series suﬃciently. Therefore, the mRSM presents rich dynamics and good sparsity. Furthermore, it avoids overfitting, and improves the predictive accuracy. Simulation results, based on two multivariate time series, substantiate the effectiveness of the mRSM.%针对多元混沌时间序列预测存在的过拟合问题及高维输入变量冗余问题，提出一种新型的多变量稀疏化预测模型—多元相关状态机。该模型采用主成分分析方法对相空间重构后的高维输入变量进行低维表示，将动态储备池作为相关向量机的核函数，充分映射多元混沌时间序列的动力学特性，使得模型具有丰富的动态机制和良好的稀疏性能，有效避免过拟合问题，提高预测精度。基于两组多元混沌时间序列的仿真实验验证了模型的有效性。
Parameter identification of time-delay chaotic system using chaotic ant swarm
International Nuclear Information System (INIS)
The identification problem of delay time as well as parameters of time-delay chaotic system is investigated in this paper. The identification problem is converted to that of parameter optimization by constructing suitable fitness function. A novel optimization method, called CAS (chaotic ant swarm), which simulates the chaotic behavior of single ant and the self-organization behavior of ant colony, is used to solve this optimization problem. Illustrative example demonstrates the effectiveness of the proposed method.
Detecting temporal and spatial correlations in pseudoperiodic time series
Zhang, Jie; Luo, Xiaodong; Nakamura, Tomomichi; Sun, Junfeng; Small, Michael
2007-01-01
Recently there has been much attention devoted to exploring the complicated possibly chaotic dynamics in pseudoperiodic time series. Two methods [Zhang , Phys. Rev. E 73, 016216 (2006); Zhang and Small, Phys. Rev. Lett. 96, 238701 (2006)] have been forwarded to reveal the chaotic temporal and spatial correlations, respectively, among the cycles in the time series. Both these methods treat the cycle as the basic unit and design specific statistics that indicate the presence of chaotic dynamics. In this paper, we verify the validity of these statistics to capture the chaotic correlation among cycles by using the surrogate data method. In particular, the statistics computed for the original time series are compared with those from its surrogates. The surrogate data we generate is pseudoperiodic type (PPS), which preserves the inherent periodic components while destroying the subtle nonlinear (chaotic) structure. Since the inherent chaotic correlations among cycles, either spatial or temporal (which are suitably characterized by the proposed statistics), are eliminated through the surrogate generation process, we expect the statistics from the surrogate to take significantly different values than those from the original time series. Hence the ability of the statistics to capture the chaotic correlation in the time series can be validated. Application of this procedure to both chaotic time series and real world data clearly demonstrates the effectiveness of the statistics. We have found clear evidence of chaotic correlations among cycles in human electrocardiogram and vowel time series. Furthermore, we show that this framework is more sensitive to examine the subtle changes in the dynamics of the time series due to the match between PPS surrogate and the statistics adopted. It offers a more reliable tool to reveal the possible correlations among cycles intrinsic to the chaotic nature of the pseudoperiodic time series.
Projective Synchronization in Time-Delayed Chaotic Systems
Institute of Scientific and Technical Information of China (English)
FENG Cun-Fang; ZHANG Yan; WANG Ying-Hai
2006-01-01
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous wort, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinite-dimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.
Phase synchronization of coupled chaotic multiple time scales systems
International Nuclear Information System (INIS)
The brushless dc motor (BLDCM) with multi-time scales is an electric machine. By coupled BLDCM, it is discovered that chaotic routes of the uncoupled systems influence synchronous result of coupled identical and nonidentical chaotic systems. Another multi-time scales form, Hindmarsh-Rose (HR) neurons, when the chaotic parameter is selected only in the range of the period-doubling route to chaos, phase synchronization can be predicted via Laypunov exponent. Finally, Laypunov exponent however cannot be used as a criterion for phase synchronization of coupled chaotic systems with either single or multi-time scales in our study
Yulmetyev, R M; Emelyanova, N; Gafarov, F; Hänggi, P; Yulmetyev, Renat; Demin, Sergey; Emelyanova, Natalya; Gafarov, Fail; Hanggi, Peter
2003-01-01
In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes. The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year oulds), young people (from 21 up to 29 year oulds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused b...
Institute of Scientific and Technical Information of China (English)
李瑞国; 张宏立; 范文慧; 王雅
2015-01-01
Chaos phenomenon which exists widely in nature and society affects people’s production and life. It has great important significance to find out the regularity of chaotic time series from a chaotic system. Since chaotic system has extremely complex dynamic characteristics and unpredictability, and chaotic time series prediction through traditional methods has low prediction precision, slow convergence speed and complex model structure, a prediction model about Hermite orthogonal basis neural network based on improved teaching-learning-based optimization algorithm is proposed. Firstly, according to the chaotic time series, autocorrelation method and Cao method are used to determine the best delay time and the minimum embedding dimension respectively, then a phase space is reconstructed to obtain the refactoring delay time vector. Secondly, on the basis of phase space reconstruction and best square approximation theory, combined with the neural network topology, a prediction model about Hermite orthogonal basis neural network with excitation functions based on the Hermite orthogonal basis functions is put forward. Thirdly, in order to optimize the parameters of the prediction model, an improved teaching-learning-based optimization algorithm is proposed, where a feedback stage is introduced at the end of the learning stage based on the teaching-learning-based optimization algorithm. Finally, the parameter optimization problem is transformed into a function optimization problem in the multidimensional space, then the improved teaching-learning-based optimization algorithm is used for parameter optimization of the prediction model so as to establish it and analyze it. Lorenz and Liu chaotic systems are taken as models respectively, then the chaotic time series which will be used as simulation object is produced by the fourth order Runge-Kutta method. The comparison experiments with other prediction models are conducted on single-step and multi-step prediction for the
Linear generalized synchronization of continuous-time chaotic systems
International Nuclear Information System (INIS)
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification
Linear generalized synchronization of continuous-time chaotic systems
Lu Jun
2003-01-01
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.
Linear generalized synchronization of continuous-time chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Lu Junguo E-mail: jglu@sjtu.edu.cn; Xi Yugeng
2003-08-01
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.
Towards pattern generation and chaotic series prediction with photonic reservoir computers
Antonik, Piotr; Hermans, Michiel; Duport, François; Haelterman, Marc; Massar, Serge
2016-03-01
Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals that is particularly well suited for analog implementations. Our team has demonstrated several photonic reservoir computers with performance comparable to digital algorithms on a series of benchmark tasks such as channel equalisation and speech recognition. Recently, we showed that our opto-electronic reservoir computer could be trained online with a simple gradient descent algorithm programmed on an FPGA chip. This setup makes it in principle possible to feed the output signal back into the reservoir, and thus highly enrich the dynamics of the system. This will allow to tackle complex prediction tasks in hardware, such as pattern generation and chaotic and financial series prediction, which have so far only been studied in digital implementations. Here we report simulation results of our opto-electronic setup with an FPGA chip and output feedback applied to pattern generation and Mackey-Glass chaotic series prediction. The simulations take into account the major aspects of our experimental setup. We find that pattern generation can be easily implemented on the current setup with very good results. The Mackey-Glass series prediction task is more complex and requires a large reservoir and more elaborate training algorithm. With these adjustments promising result are obtained, and we now know what improvements are needed to match previously reported numerical results. These simulation results will serve as basis of comparison for experiments we will carry out in the coming months.
An Optimized Multikeying Chaotic Encryption for Real Time Applications
Directory of Open Access Journals (Sweden)
R. Tamijetchelvy
2013-12-01
Full Text Available In recent years, the availability of wireless technologies has become prominent solution for next generation wireless networks (NGWN. Hence the demand for secure communication is an important research issue. Cryptography is recognized as the best method of data protection against active and passive attacks. Therefore a novel chaotic cryptographic scheme is proposed for real time communication. Chaos signals are random behaviour, continuous and sensitive dependence on initial conditions. However, it has been shown that most of these chaotic methods have a low level of security because of single keying concept. In this paper an optimized fast encryption scheme based on chaotic signal with multi key is justified for video frame. Simulation results show that the proposed chaotic encryption scheme outperforms the existing scheme in terms of considerable reduction in encryption and decryption time. The security of the proposed scheme is also analysed by various cryptanalysis attacks.
Recurrence time statistics in chaotic dynamics. I. Discrete time maps
International Nuclear Information System (INIS)
The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markov maps the recurrence problem is cast into a renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values
Impulsive Control of Memristive Chaotic Systems with Impulsive Time Window
Directory of Open Access Journals (Sweden)
FuLi Chen
2015-01-01
Full Text Available The problem of impulsive control for memristor-based chaotic circuit systems with impulsive time windows is investigated. Based on comparison principle, several novel criteria which guarantee the asymptotic stabilization of the memristor-based chaotic circuit systems are obtained. In comparison with previous results, the present results are easily verified. Numerical simulations are given to further illustrate the effectiveness of the theoretical results.
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
da Silva, R. M.; Manchein, C.; Beims, M. W.; Altmann, E. G.
2015-01-01
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying ...
DEFF Research Database (Denmark)
Moskowitz, Tobias J.; Ooi, Yao Hua; Heje Pedersen, Lasse
2012-01-01
We document significant “time series momentum” in equity index, currency, commodity, and bond futures for each of the 58 liquid instruments we consider. We find persistence in returns for one to 12 months that partially reverses over longer horizons, consistent with sentiment theories of initial...... 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....
Loredo, Thomas
The key, central objectives of the proposed Time Series Explorer project are to develop an organized collection of software tools for analysis of time series data in current and future NASA astrophysics data archives, and to make the tools available in two ways: as a library (the Time Series Toolbox) that individual science users can use to write their own data analysis pipelines, and as an application (the Time Series Automaton) providing an accessible, data-ready interface to many Toolbox algorithms, facilitating rapid exploration and automatic processing of time series databases. A number of time series analysis methods will be implemented, including techniques that range from standard ones to state-of-the-art developments by the proposers and others. Most of the algorithms will be able to handle time series data subject to real-world problems such as data gaps, sampling that is otherwise irregular, asynchronous sampling (in multi-wavelength settings), and data with non-Gaussian measurement errors. The proposed research responds to the ADAP element supporting the development of tools for mining the vast reservoir of information residing in NASA databases. The tools that will be provided to the community of astronomers studying variability of astronomical objects (from nearby stars and extrasolar planets, through galactic and extragalactic sources) will revolutionize the quality of timing analyses that can be carried out, and greatly enhance the scientific throughput of all NASA astrophysics missions past, present, and future. The Automaton will let scientists explore time series - individual records or large data bases -- with the most informative and useful analysis methods available, without having to develop the tools themselves or understand the computational details. Both elements, the Toolbox and the Automaton, will enable deep but efficient exploratory time series data analysis, which is why we have named the project the Time Series Explorer. Science
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.; Jónsson, P.; Kuusisto, E.; Larsen, S. E.; Lindström, G.; Ovesen, N. B.; Roald, L. A.
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)
Fischer, Paul; Hilbert, Astrid
2012-01-01
We introduce a platform which supplies an easy-to-handle, interactive, extendable, and fast analysis tool for time series analysis. In contrast to other software suits like Maple, Matlab, or R, which use a command-line-like interface and where the user has to memorize/look-up the appropriate...... 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...... choose between manual and automated parameter selection. The user can dene new transformations and add them to the system. The application contains efficient implementations of advanced and recent techniques for time series analysis including techniques related to extreme value analysis and filtering...
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)""…
Network structure of multivariate time series
Lacasa, Lucas; Nicosia, Vincenzo; Latora, Vito
2015-10-01
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.
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...
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-09-01
In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.
Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control
International Nuclear Information System (INIS)
By the method of quadratic optimum control, a quadratic optimal regulator is used for synchronizing two complex chaotic systems in series form. By this method the least error with less control energy is achieved, and the optimization on both energy and error is realized synthetically. The simulation results of two Quantum-CNN chaos systems in series form prove the effectiveness of this method. Finally, chaotization of the system is given by optimal control.
Complete chaotic synchronization in mutually coupled time-delay systems.
Landsman, Alexandra S; Schwartz, Ira B
2007-02-01
Complete chaotic synchronization of end lasers has been observed in a line of mutually coupled, time-delayed system of three lasers, with no direct communication between the end lasers. The present paper uses ideas from generalized synchronization to explain the complete synchronization in the presence of long coupling delays, applied to a model of mutually coupled semiconductor lasers in a line. These ideas significantly simplify the analysis by casting the stability in terms of the local dynamics of each laser. The variational equations near the synchronization manifold are analyzed, and used to derive the synchronization condition that is a function of parameters. The results explain and predict the dependence of synchronization on various parameters, such as time delays, strength of coupling and dissipation. The ideas can be applied to understand complete synchronization in other chaotic systems with coupling delays and no direct communication between synchronized subsystems. PMID:17358399
International Nuclear Information System (INIS)
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the non-trivial dynamics of the task list. The model is characterized by a priority distribution as an input parameter, which describes the choice procedure from the list. We give exact results on the asymptotic behaviour of the model and we show that the interevent time distribution is power-law decaying for any kind of input distributions that remain normalizable in the infinite list limit, with exponents tunable between 1 and 2. The model satisfies a scaling law between the exponents of interevent time distribution (β) and autocorrelation function (α): α + β = 2. This law is general for renewal processes with power-law decaying interevent time distribution. We conclude that slowly decaying autocorrelation function indicates long-range dependence only if the scaling law is violated. (paper)
The synchronization for time-delay of linearly bidirectional coupled chaotic system
International Nuclear Information System (INIS)
Based on Lyapunov stability theory and matrix measure, this paper presents a new generic criterion of global chaotic synchronization for bidirectional coupled chaotic system with time-delay. A new chaotic system with four-scroll attractor is chosen as an example to verify the effectiveness of the criterion. Numerical simulation are shown for demonstration
Time evolution of frequency components in a chaotic digital signal
Martin-Pereda, Jose A.; Gonzalez-Marcos, Ana P.
2001-11-01
The type of signals obtained has conditioned chaos analysis tools. Almost in every case, they have analogue characteristics. But in certain cases, a chaotic digital signal is obtained and theses signals need a different approach than conventional analogue ones. The main objective of this paper will be to present some possible approaches to the study of this signals and how information about their characteristics may be obtained in the more straightforward possible way. We have obtained digital chaotic signals from an Optical Logic Cell with some feedback between output and one of the possible control gates. This chaos has been reported in several papers and its characteristics have been employed as a possible method to secure communications and as a way to encryption. In both cases, the influence of some perturbation in the transmission medium gave problems both for the synchronization of chaotic generators at emitter and receiver and for the recovering of information data. A proposed way to analyze the presence of some perturbation is to study the noise contents of transmitted signal and to implement a way to eliminate it. In our present case, the digital signal will be converted to a multilevel one by grouping bits in packets of 8 bits and applying conventional methods of time-frequency analysis to them. The results give information about the change in signals characteristics and hence some information about the noise or perturbations present. Equivalent representations to the phase and to the Feigenbaum diagrams for digital signals are employed in this case.
Determination of Optimal Control Strength of Delayed Feedback Control Using Time Series
Institute of Scientific and Technical Information of China (English)
YIN Hua-Wei; LU Wei-Ping; WANG Peng-Ye
2004-01-01
@@ We study controlling chaos using time-delayed feedback control based on chaotic time series without prior knowl edge of dynamical systems, and determine the optimal control parameters for stabilizing unstable periodic orbits with maximal stability.
Application of bootstrap to detecting chaos in financial time series
Brzozowska-Rup, Katarzyna; Orłowski, Arkadiusz
2004-12-01
A moving blocks bootstrap procedure is used to investigate the dynamics of nominal exchange rates and the return rates of the US Dollar against the Polish Zloty. The problem if these financial time series exhibit chaotic behavior is undertaken. A possibility of detecting the presence of a positive Lyapunov exponent is studied.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-07-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
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
Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels
Directory of Open Access Journals (Sweden)
Marcio Eisencraft
2009-01-01
Full Text Available Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.
A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
LI LI-XIANG; PENG HAI-PENG; GUAN BAO-ZHU; XU JIN-MING
2001-01-01
We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.
Time scales and species coexistence in chaotic flows
Galla, Tobias
2016-01-01
Empirical observations in marine ecosystems have suggested a balance of biological and advection time scales as a possible explanation of species coexistence. To characterise this scenario, we measure the time to fixation in neutrally evolving populations in chaotic flows. Contrary to intuition the variation of time scales does not interpolate straightforwardly between the no-flow and well-mixed limits; instead we find that fixation is the slowest at intermediate Damk\\"ohler numbers, indicating long-lasting coexistence of species. Our analysis shows that this slowdown is due to spatial organisation on an increasingly modularised network. We also find that diffusion can either slow down or speed up fixation, depending on the relative time scales of flow and evolution.
多元混沌时间序列的因子回声状态网络预测模型%Factor Echo State Network for Multivariate Chaotic Time Series Prediction
Institute of Scientific and Technical Information of China (English)
许美玲; 韩敏
2015-01-01
When an echo state network is used to predict mul-tivariate time series, there may exist ill-posed problem. This pa-per proposes a novel prediction model, named factor echo state network, to solve the problem. It uses a factor analysis (FA) al-gorithm to extract the common factors of the reservoir matrix, and to remove the redundancies and noises. Then the unknown output weights are calculated by linear regression of the output and common factors. The model is used to predict Lorenz series and monthly average temperature-rainfall time series in Dalian, and simulation results substantiate its effectiveness.%针对采用回声状态网络预测多元混沌时间序列时存在的病态解问题,本文建立了因子回声状态网络模型,通过因子分析(Factor analysis, FA)方法提取高维储备池状态矩阵的公因子,去除冗余和噪声成分。利用降维后的因子变量与期望输出之间的线性回归关系,求解网络未知参数。基于Lorenz 序列和大连月平均气温–降雨量的仿真实验验证了本文所提模型的有效性。
Finite-Time Synchronizing Control for Chaotic Neural Networks
Directory of Open Access Journals (Sweden)
Chao Zhang
2014-01-01
Full Text Available This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.
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...
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.
LM algorithm in echo state network for chaotic time series prediction%回声状态网络LM算法及混沌时间序列预测
Institute of Scientific and Technical Information of China (English)
韩敏; 穆大芸
2011-01-01
The problem of sigular solution in echo state network（ESN） learning algorithm is existed,which is easy to cause ill issue.Especially when training samples are less than the dimenssions of the output,the solution of the ESN must be singular.Therefore,Levenberg Marquardt（LM） algorithm is used to learn ESN instead of linear regression method,which can effectively control the amplitude of the output weight result in improved predictive performance.The presented model is tested on the Lorenz time series and applied to some real life time series such as Dalian monthly average temprture time series.Actual simulation results show that the predictive model has higher predictive accuracy,and is of great practicality and effectiveness.%回声状态网络（ESN）学习算法中可能存在解的奇异问题,在时间序列预测时易导致病态解问题,且伴随着具有较大幅值的输出权值,尤其是当训练样本个数小于输出权值维数时,ESN的解必为奇异的.鉴于此,考虑使用LM（Levenberg Marquardt）算法代替常用的线性回归方法,自适应选择LM参数,从而有效地控制输出权值的幅值,提高ESN的预测性能.通过Lorenz混沌时间序列进行预测研究,对大连月平均气温实际数据进行仿真研究,取得了较好的预测效果.
Bootstrapping High Dimensional Time Series
Zhang, Xianyang; Cheng, Guang
2014-01-01
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for mean vector; (2) specification testing on the second order property of time series such as white noise testing and bandedness testing of covariance matrix; (3) specification testing on the spectral property of time series. In theory, we first derive a Gaussi...
Autoencoding Time Series for Visualisation
Gianniotis, Nikolaos; Kügler, Dennis; Tino, Peter; Polsterer, Kai; Misra, Ranjeev
2015-01-01
We present an algorithm for the visualisation of time series. To that end we employ echo state networks to convert time series into a suitable vector representation which is capable of capturing the latent dynamics of the time series. Subsequently, the obtained vector representations are put through an autoencoder and the visualisation is constructed using the activations of the bottleneck. The crux of the work lies with defining an objective function that quantifies the reconstruction error ...
Allan, Alasdair
2014-06-01
FROG performs time series analysis and display. It provides a simple user interface for astronomers wanting to do time-domain astrophysics but still offers the powerful features found in packages such as PERIOD (ascl:1406.005). FROG includes a number of tools for manipulation of time series. Among other things, the user can combine individual time series, detrend series (multiple methods) and perform basic arithmetic functions. The data can also be exported directly into the TOPCAT (ascl:1101.010) application for further manipulation if needed.
Multi-target real-time ranging with chaotic laser radar
Institute of Scientific and Technical Information of China (English)
Bingjie Wang; Yuncai Wang; Lingqin Kong; Anbang Wang
2008-01-01
We demonstrate the feasibility of multi-target real-time ranging with a chaotic laser radar. The used chaotic laser is emitted by a semiconductor laser with optical feedback. We design a proof-of-concept experiment based on the correlation detection and realize the range measurements of two targets simultaneously. The range resolution of 9 cm between two targets is achieved, which is limited by the bandwidth of the used real-time oscilloscope. A preliminary experiment of chaotic laser coherence is carried out to verify the high resolution of the chaotic lidar.
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.
A unified approach for impulsive lag synchronization of chaotic systems with time delay
International Nuclear Information System (INIS)
In this paper, we propose a unified approach for impulsive lag-synchronization of a class of chaotic systems with time delay by employing the stability theory of impulsive delayed differential equations. Three well-known delayed chaotic systems are presented to illustrate our results. Also, the estimates of the stable regions for these systems are given, respectively
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
Autoencoding Time Series for Visualisation
Gianniotis, Nikolaos; Tino, Peter; Polsterer, Kai; Misra, Ranjeev
2015-01-01
We present an algorithm for the visualisation of time series. To that end we employ echo state networks to convert time series into a suitable vector representation which is capable of capturing the latent dynamics of the time series. Subsequently, the obtained vector representations are put through an autoencoder and the visualisation is constructed using the activations of the bottleneck. The crux of the work lies with defining an objective function that quantifies the reconstruction error of these representations in a principled manner. We demonstrate the method on synthetic and real data.
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.
A Chaotic Block Cipher for Real-Time Multimedia
Directory of Open Access Journals (Sweden)
M. Venkatesulu
2012-01-01
Full Text Available Problem statement: The widespread use of image, audio and video data makes media content protection increasingly necessary and important. We propose a naive approach which treats the multimedia signal to be protected as a text and use proposed encryption design to encrypt the whole data stream. Upon reception, the entire cipher text data stream would be decrypted and playback can be performed at the client end with an initial time delay. Approach: We introduce a block cipher algorithm, which encrypts and decrypts a block size of 512 bits regardless of the file format. In this, a permutation algorithm using a chaotic system is employed to provide the shuffler function. A shuffler operator is defined using the shuffler function. A random key generator generates key sequences and the scheme employs key-dependant transformations based on distance in the shuffling operator. The process of encryption/decryption is governed by the shuffler function, shuffler operator and the pseudorandom key. Results: The basic operation used is logical XOR and so the algorithm has a very high encryption/decryption speed. The execution time shows the proposed scheme is faster than the existing cryptographic schemes. Conclusion: The proposal of the algorithm is to manage the tradeoffs between the speed and security and hence appropriate for real-time image and video communication applications.
Lag synchronization of chaotic systems with time-delayed linear terms via impulsive control
Indian Academy of Sciences (India)
Ranchao Wu; Dongxu Cao
2013-11-01
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems. Numerical simulations on time-delayed Lorenz and hyperchaotic Chen systems are also carried out to show the effectiveness of the proposed scheme. Note that under the scheme the chaotic system is controlled only at discrete time instants, and so it reduces the control cost in real applications.
Synchronisation of fractional-order time delayed chaotic systems with ring connection
He, S.; Sun, K.; Wang, H.
2016-02-01
In this paper, synchronisation of fractional-order time delayed chaotic systems in ring networks is investigated. Based on Lyapunov stability theory, a new generic synchronisation criterion for N-coupled chaotic systems with time delay is proposed. The synchronisation scheme is applied to N-coupled fractional-order time delayed simplified Lorenz systems, and the Adomian decomposition method (ADM) is developed for solving these chaotic systems. Performance analysis of the synchronisation network is carried out. Numerical experiments demonstrate that synchronisation realises in both state variables and intermediate variables, which verifies the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
Multivariate Time Series Similarity Searching
Jimin Wang; Yuelong Zhu; Shijin Li; Dingsheng Wan; Pengcheng Zhang
2014-01-01
Multivariate time series (MTS) datasets are very common in various financial, multimedia, and hydrological fields. In this paper, a dimension-combination method is proposed to search similar sequences for MTS. Firstly, the similarity of single-dimension series is calculated; then the overall similarity of the MTS is obtained by synthesizing each of the single-dimension similarity based on weighted BORDA voting method. The dimension-combination method could use the existing similarity searchin...
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕
2001-01-01
The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied,the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. The results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable.
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. PMID:23277606
Symplectic geometry spectrum regression for prediction of noisy time series
Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie
2016-05-01
We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay
Levnajić, Zoran; Tadić, Bosiljka
2007-01-01
We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic motion, the coupled map system exhibits variety of dynamical effects in a wide range of coupling strengths. This includes dynamical localization, emergent periodicity, and appearance of strange non-chaotic attractors. Near the strange attractors we find long-rang...
Adaptive control of chaotic systems with stochastic time varying unknown parameters
International Nuclear Information System (INIS)
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment
Estimating measurement noise in a time series by exploiting nonstationarity
International Nuclear Information System (INIS)
A measured time series is always corrupted by noise to some degree. Even a rough estimation of the level of noise contained in an experimental time series is valuable. This is so, for example, when one wishes to apply techniques from nonlinear dynamics theory to analyze a time series. However, this is a very difficult problem. It becomes even harder when the measured signal is nonstationary, which is often true in practice. Detecting nonstationarity has been a hot research topic in recent years. However, many researchers stop when they find the time series under study is indeed nonstationary. Here, we exploit the very nature of nonstationarity in a signal to formulate a method for quantitatively estimating the amount of noise contained in the signal. The approach is first verified using computer simulated signals based on the chaotic Lorenz attractors and the Mackey-Glass equations with different parameters and then applied to the clinically measured intracranial EEG signals. It is found that the amount of noise in the EEG signals is around 8.0-8.5% in terms of amplitude. Implications to whether EEG signals are chaotic or not are discussed
Global synchronization criteria with channel time-delay for chaotic time-delay system
International Nuclear Information System (INIS)
Based on the Lyapunov stabilization theory, matrix measure, and linear matrix inequality (LMIs), this paper studies the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. Some generic conditions of chaos synchronization with time-delay in the transmission channel is established. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criteria under which the global chaos synchronization of the time-delay coupled systems is achieved
Global synchronization criteria with channel time-delay for chaotic time-delay system
Energy Technology Data Exchange (ETDEWEB)
Sun Jitao E-mail: sunjt@sh163.net
2004-08-01
Based on the Lyapunov stabilization theory, matrix measure, and linear matrix inequality (LMIs), this paper studies the chaos synchronization of time-delay system using the unidirectional linear error feedback coupling with time-delay. Some generic conditions of chaos synchronization with time-delay in the transmission channel is established. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criteria under which the global chaos synchronization of the time-delay coupled systems is achieved.
Stochastic Time-Series Spectroscopy
Scoville, John
2015-01-01
Spectroscopically measuring low levels of non-equilibrium phenomena (e.g. emission in the presence of a large thermal background) can be problematic due to an unfavorable signal-to-noise ratio. An approach is presented to use time-series spectroscopy to separate non-equilibrium quantities from slowly varying equilibria. A stochastic process associated with the non-equilibrium part of the spectrum is characterized in terms of its central moments or cumulants, which may vary over time. This parameterization encodes information about the non-equilibrium behavior of the system. Stochastic time-series spectroscopy (STSS) can be implemented at very little expense in many settings since a series of scans are typically recorded in order to generate a low-noise averaged spectrum. Higher moments or cumulants may be readily calculated from this series, enabling the observation of quantities that would be difficult or impossible to determine from an average spectrum or from prinicipal components analysis (PCA). This meth...
Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards
Veble, G.; Prosen, T.; Robnik, M.
2007-01-01
We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.
Chaotic anti-control for the bounded linear continuous-time system
Institute of Scientific and Technical Information of China (English)
Li Jianfen; Lin Hui; Li Nong
2008-01-01
With regard to the bounded linear continuous-time system, a universal chaotic anti-controlling method was presented on the basis of tracking control. A tracking controller is designed to such an extent that it can track any chaotic reference input, thus making it possible to chaotify the linear system. The controller is identical in structure for different controlled linear systems. Computer simulations proved the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Y. Saiki
2007-09-01
Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.
Time evolution of frequency components In a chaotic digital signal
Martín Pereda, José Antonio; González Marcos, Ana
2001-01-01
The type of signals obtained has conditioned chaos analysis tools. Almost in every case, they have analogue characteristics. But in certain cases, a chaotic digital signal is obtained and theses signals need a different approach than conventional analogue ones. The main objective of this paper will be to present some possible approaches to the study of this signals and how information about their characteristics may be obtained in the more straightforward possible way. We have obtained digita...
Lyapunov exponents from CHUA's circuit time series using artificial neural networks
Gonzalez, J. Jesus; Espinosa, Ismael E.; Fuentes, Alberto M.
1995-01-01
In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.
Detection of "noisy" chaos in a time series
DEFF Research Database (Denmark)
Chon, K H; Kanters, J K; Cohen, R J; Holstein-Rathlou, N H
Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both 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......, 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...
Institute of Scientific and Technical Information of China (English)
张学清; 梁军
2013-01-01
According to the chaotic feature of wind power time series, a combined short-term wind power forecasting approach based on ensemble empirical mode decomposition (EEMD)-approximate entropy and echo state network (ESN) is proposed. Firstly, in order to reduce the calculation scale of partial analysis for wind power and improve the wind power prediction accuracy, the wind power time series is decomposed into a series of wind power subsequences with obvious differences in complex degree by using EEMD-approximate entropy. Then, the forecasting model of each subsequence is created with least squares support vector machine (LSSVM), ESN and EEMD-ESN improved with the regularized high frequency parts. Finally, the simulation is performed by using the real data collected from a certain wind farm, the results show that the EEMD-ESN model is better in the training speed and forecasting accuracy, than those obtained from the least square support vector machine (LSSVM) model, which provides a new useful reference for the short-term forecasting of wind power in online engineering application.% 针对风电功率时间序列的混沌特性,提出了一种基于集成经验模态分解(ensemble empirical mode decomposition, EEMD)-近似熵和回声状态网络(echo state network, ESN)的风电功率混沌时间序列组合预测模型。首先为降低对风电功率局部分析的计算规模以及提高预测的准确性,利用EEMD-近似熵将风电功率时间序列分解为一系列复杂度差异明显的风电子序列；然后对各子序列分别建立ESN、经过高频分量正则化改进的EEMD-ESN模型和最小二乘支持向量机预测模型；最后以某一风电场实际采集的数据为算例,仿真结果表明EEMD-ESN模型在训练速度和预测精度上优于最小二乘支持向量机模型,为实现风电功率短期预测的在线工程应用提供了新的有益参考。
Response of the parameters of a neural network to pseudoperiodic time series
Zhao, Yi; Weng, Tongfeng; Small, Michael
2014-02-01
We propose a representation plane constructed from parameters of a multilayer neural network, with the aim of characterizing the dynamical character of a learned time series. We find that fluctuation of this plane reveals distinct features of the time series. Specifically, a periodic representation plane corresponds to a periodic time series, even when contaminated with strong observational noise or dynamical noise. We present a theoretical explanation for how the neural network training algorithm adjusts parameters of this representation plane and thereby encodes the specific characteristics of the underlying system. This ability, which is intrinsic to the architecture of the neural network, can be employed to distinguish the chaotic time series from periodic counterparts. It provides a new path toward identifying the dynamics of pseudoperiodic time series. Furthermore, we extract statistics from the representation plane to quantify its character. We then validate this idea with various numerical data generated by the known periodic and chaotic dynamics and experimentally recorded human electrocardiogram data.
The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system
International Nuclear Information System (INIS)
Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed
Adaptive control of uncertain time-delay chaotic systems
Institute of Scientific and Technical Information of China (English)
Zhuhong ZHANG
2005-01-01
This work investigates adaptive control of a large class of uncertain me-delay chaotic systems (UTCSs) with unknown general perturbation terms bounded by a polynomial ( unknown gains). Associated with the different cases of known and unknown system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequalities (LMI) which can be solved easily by convex optimization algorithms. Two examples are used for examining the effectiveness of the proposed methods.
Learning time series evolution by unsupervised extraction of correlations
International Nuclear Information System (INIS)
As a consequence, we are able to model chaotic and nonchaotic time series. Furthermore, one critical point in modeling time series is the determination of the dimension of the embedding vector used, i.e., the number of components of the past that are needed to predict the future. With this method we can detect the embedding dimension by extracting the influence of the past on the future, i.e., the correlation of remote past and future. Optimal embedding dimensions are obtained for the Henon map and the Mackey-Glass series. When noisy data corrupted by colored noise are used, a model is still possible. The noise will then be decorrelated by the network. In the case of modeling a chemical reaction, the most natural architecture that conserves the volume is a symplectic network which describes a system that conserves the entropy and therefore the transmitted information
Lee, C; Zhu, X; Gao, K; Hai, W; Duan Yi Shi; Liu, W K; Lee, Chaohong; Shi, Lei; Zhu, Xiwen; Gao, Kelin; Hai, Wenhua; Duan, Yiwu; Liu, Wing-Ki
2001-01-01
We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary condition indicates that the Melnikov function is equal to zero, so the stable oscillations are Melnikov chaotic. For the ordinary parameters and initial conditions, the chaotic dynamics is simulated with numerical calculation. If the damping is absent, with the increasing of the trap asymmetry, the regular oscillations become chaotic gradually, the corresponding stroboscopic Poincare sections (SPS) vary from a single island to more islands, and then the chaotic sea. For the completely chaotic oscillations, the long-term localiza...
Parameter estimation for time-delay chaotic system by particle swarm optimization
International Nuclear Information System (INIS)
The knowledge about time delays and parameters is very important for control and synchronization of time-delay chaotic system. In this paper, parameter estimation for time-delay chaotic system is given by treating the time delay as an additional parameter. The parameter estimation is converted to an optimization problem, which finds a best parameter combination such that an objective function is minimized. Particle swarm optimization (PSO) is used to optimize the objective function through particles' cooperation and evolution. Two illustrative examples are given to show the validity of the proposed method.
ACCURATE TIME SERIES CLASSIFICATION USING SHAPELETS
M. Arathi; A. GOVARDHAN
2014-01-01
Time series data are sequences of values measured o ver time. One of the most recent approaches to classification of time series data is to find shape lets within a data set. Time series shapelets are time series subsequences which represent a class. In order to compare two time series sequences, existing work use s Euclidean distance measure. The problem with Euclid ean distance is that it requires data to be standardized if scales ...
Nonlinear time series analysis methods and applications
Diks, Cees
1999-01-01
Methods of nonlinear time series analysis are discussed from a dynamical systems perspective on the one hand, and from a statistical perspective on the other. After giving an informal overview of the theory of dynamical systems relevant to the analysis of deterministic time series, time series generated by nonlinear stochastic systems and spatio-temporal dynamical systems are considered. Several statistical methods for the analysis of nonlinear time series are presented and illustrated with applications to physical and physiological time series.
Experimental observation of Loschmidt time reversal of a Quantum Chaotic System
Ullah, A; Hoogerland, M. D.
2009-01-01
We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic deBroglie waves. We use ultra cold atoms from a Bose-Einstein condensate in a quantum $\\delta$-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of "chaotic" evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the...
Directory of Open Access Journals (Sweden)
P. Siricharuanun
2016-01-01
Full Text Available A second-order sliding mode control for chaotic synchronization with bounded disturbance is studied. A robust finite-time controller is designed based on super twisting algorithm which is a popular second-order sliding mode control technique. The proposed controller is designed by combining an adaptive law with super twisting algorithm. New results based on adaptive super twisting control for the synchronization of identical Qi three-dimensional four-wing chaotic system are presented. The finite-time convergence of synchronization is ensured by using Lyapunov stability theory. The simulations results show the usefulness of the developed control method.
Reconstruction of Ordinary Differential Equations From Time Series Data
Mai, Manuel; O'Hern, Corey S
2016-01-01
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We show that employing sparse representations provides more accurate ODE reconstruction compared to least-squares reconstruction techniques for a given amount of time series data. We test and validate the ODE reconstruction method on known 1D, 2D, and 3D systems of ODEs. The 1D system possesses two stable fixed points; the 2D system possesses an oscillatory fixed point with closed orbits; and the 3D system displays chaotic dynamics on a strange attractor. We determine the amount of data required to achieve an error in the reconstructed functions to less than $0.1\\%$. For the reconstructed 1D and 2D systems, we are able to match the trajectories from the original ODEs even at long times. For the 3D system with chaotic dynamics, as expected, the trajectories from the original an...
Yang, Dong-Sheng; Liu, Zhen-Wei; Zhao, Yan; Liu, Zhao-Bing
2012-04-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.
International Nuclear Information System (INIS)
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method. (general)
Finite-time synchronization of a class of autonomous chaotic systems
Indian Academy of Sciences (India)
Huini Lin; Jianping Cai
2014-03-01
Some criteria for achieving the finite-time synchronization of a class of autonomous chaotic systems are derived by the finite-time stability theory and Gerschgorin disc theorem. Numerical simulations are shown to illustrate the effectiveness of the proposed method.
Chaos analysis of the electrical signal time series evoked by acupuncture
International Nuclear Information System (INIS)
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed
Chaos analysis of the electrical signal time series evoked by acupuncture
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China)]. E-mail: jiangwang@tju.edu.cn; Sun Li [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Fei Xiangyang [School of Electrical Engineering, Tianjin University, Tianjin 300072 (China); Zhu Bing [Institute of Acupuncture and Moxibustion, China Academy of Traditional Chinese Medicine, Beijing 100700 (China)
2007-08-15
This paper employs chaos theory to analyze the time series of electrical signal which are evoked by different acupuncture methods applied to the Zusanli point. The phase space is reconstructed and the embedding parameters are obtained by the mutual information and Cao's methods. Subsequently, the largest Lyapunov exponent is calculated. From the analyses we can conclude that the time series are chaotic. In addition, differences between various acupuncture methods are discussed.
Institute of Scientific and Technical Information of China (English)
Yang Dong-Sheng; Liu Zhen-Wei; Zhao Yan; Liu Zhao-Bing
2012-01-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory,a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a timevarying communication topology connection.The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory.The derived novel criteria are in the form of linear matrix inequalities (LMIs),which are easy to examine and tremendously reduce the computation burden from the feedback matrices.This paper provides an alternative networked secure communication scheme which can be extended conveniently.An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.
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
Analysis of the time structure of synchronization in multidimensional chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Isochronal synchronization of time delay and delay-coupled chaotic systems
Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.
2011-04-01
This paper studies the problem of isochronal synchronization of time-delay chaotic systems featuring also coupling delay. Based on the Lyapunov-Krasovskii stability theory, sufficient conditions are derived for the stability of isochronal synchronization between a pair of identical chaotic systems. Such criteria permit the proper design of stable proportional linear feedback controller, more specifically, the design of adequate proportional feedback gain matrices. The proposed criteria are suited to systems with (i) intrinsic delay, (ii) coupling delay or (iii) both. Numerical simulations of the synchronization of delay-coupled systems are presented as examples of the application of the criteria.
Energy Technology Data Exchange (ETDEWEB)
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K., E-mail: skmahapatra@bitmesra.ac.in [Plasma Laboratory, Department of Physics, Birla Institute of Technology-Mesra, Ranchi 835215 (India); Shaw, Pankaj Kumar; Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
LMI optimization approach to stabilization of time-delay chaotic systems
International Nuclear Information System (INIS)
Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, this paper proposes a novel control method for stabilization of a class of time-delay chaotic systems. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is included to show the advantage of the result derived
A novel criterion for delayed feedback control of time-delay chaotic systems
International Nuclear Information System (INIS)
This paper investigated stability criterion of time-delay chaotic systems via delayed feedback control (DFC) using the Lyapunov stability theory and linear matrix inequality (LMI) technique. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is given to illuminate the design procedure and advantage of the result derived
Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems
Directory of Open Access Journals (Sweden)
Y. Saiki
2008-08-01
Full Text Available Unstable periodic orbit (UPO recently has become a keyword in analyzing complex phenomena in geophysical fluid dynamics and space physics. In this paper, sets of UPOs in low dimensional maps are theoretically or systematically found, and time averaged properties along UPOs are studied, in relation to those of chaotic orbits.
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...
Effective Feature Preprocessing for Time Series Forecasting
DEFF Research Database (Denmark)
Zhao, Junhua; Dong, Zhaoyang; Xu, Zhao
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...
Application of chaotic noise reduction techniques to chaotic data trained by ANN
Indian Academy of Sciences (India)
C Chandra Shekara Bhat; M R Kaimal; T R Ramamohan
2001-10-01
We propose a novel method of combining artiﬁcial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can signiﬁcantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be signiﬁcantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.
A novel memristive time-delay chaotic system without equilibrium points
Pham, V.-T.; Vaidyanathan, S.; Volos, C. K.; Jafari, S.; Kuznetsov, N. V.; Hoang, T. M.
2016-02-01
Memristor and time-delay are potential candidates for constructing new systems with complex dynamics and special features. A novel time-delay system with a presence of memristive device is proposed in this work. It is worth noting that this memristive time-delay system can generate chaotic attractors although it possesses no equilibrium points. In addition, a circuitry implementation of such time-delay system has been introduced to show its feasibility.
International Nuclear Information System (INIS)
This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach. -- Highlights: → Optimizing the synchronization time is essential for chaotic synchronization application. → This is particularly important in communication system for recovering encoded message/data. → This Letter proposes an adaptive control method for realizing finite-time chaos synchronization. → The method gives simple control inputs that guarantee finite-time synchronization. → It could be exploited for experimental realization of finite-time synchronization.
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The synchronization of chaotic neurons coupled with gap junction with time delays is investigated. In this paper, the coupled model is based on the nonlinear cable model of neuron. The influences of the strength of gap junction and the time delay on the synchronization are discussed in detail. The so called delay-dependent criteria for the synchronization of two coupled neurons which contain the information of the time delay and the coupling strength is given
International Nuclear Information System (INIS)
This paper investigates a novel stability criterion for interval time-delay chaotic systems via the evolutionary programming (EP) approach. First a delay-dependent criterion is derived for ensuring the stability of degenerate time-delay systems, and then by solving eigenvalue location optimization problems, which will be defined later, the robust stability of interval time-delay systems can be guaranteed. An example is given to verify our method that yields less conservative results than those appeared in the literature
GENERAL: Synchronization of time-delay chaotic systems on small-world networks with delayed coupling
Qi, Wei; Wang, Ying-Hai
2009-04-01
By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.
Energy Technology Data Exchange (ETDEWEB)
Wang Jiang [School of Electrical and Automation Engineering, Tianjin University, 300072, Tianjin (China)], E-mail: jiangwang@tju.edu.cn; Deng Bin; Fei Xiangyang [School of Electrical and Automation Engineering, Tianjin University, 300072, Tianjin (China)
2008-02-15
The synchronization of chaotic neurons coupled with gap junction with time delays is investigated. In this paper, the coupled model is based on the nonlinear cable model of neuron. The influences of the strength of gap junction and the time delay on the synchronization are discussed in detail. The so called delay-dependent criteria for the synchronization of two coupled neurons which contain the information of the time delay and the coupling strength is given.
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
A review of subsequence time series clustering.
Zolhavarieh, Seyedjamal; Aghabozorgi, Saeed; 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
International Nuclear Information System (INIS)
Highlights: → A chaotic model of spontaneous neuron firing. → Mapping the irregular spiking time-series into telegraph signals. → Fundamental frequency of the Rossler attractor provides periodic component. → Spiking time-series from spontaneous activity of hippocampal neurons. → Comparison shows good agreement between the model and the experiment. - Abstract: A chaotic model of spontaneous (without external stimulus) neuron firing has been analyzed by mapping the irregular spiking time-series into telegraph signals. In this model the fundamental frequency of chaotic Roessler attractor provides (with a period doubling) the strong periodic component of the generated irregular signal. The exponentially decaying broad-band part of the spectrum of the Roessler attractor has been transformed by the threshold firing mechanism into a scaling tale. These results are compared with irregular spiking time-series obtained in vitro from a spontaneous activity of hippocampal (CA3) singular neurons (rat's brain slice culture). The comparison shows good agreement between the model and experimentally obtained spectra.
Learning time series evolution by unsupervised extraction of correlations
Deco, Gustavo; Schürmann, Bernd
1995-03-01
We focus on the problem of modeling time series by learning statistical correlations between the past and present elements of the series in an unsupervised fashion. This kind of correlation is, in general, nonlinear, especially in the chaotic domain. Therefore the learning algorithm should be able to extract statistical correlations, i.e., higher-order correlations between the elements of the time signal. This problem can be viewed as a special case of factorial learning. Factorial learning may be formulated as an unsupervised redundancy reduction between the output components of a transformation that conserves the transmitted information. An information-theoretic-based architecture and learning paradigm are introduced. The neural architecture has only one layer and a triangular structure in order to transform elements by observing only the past and to conserve the volume. In this fashion, a transformation that guarantees transmission of information without loss is formulated. The learning rule decorrelates the output components of the network. Two methods are used: higher-order decorrelation by explicit evaluation of higher-order cumulants of the output distributions, and minimization of the sum of entropies of each output component in order to minimize the mutual information between them, assuming that the entropies have an upper bound given by Gibbs second theorem. After decorrelation between the output components, the correlation between the elements of the time series can be extracted by analyzing the trained neural architecture. As a consequence, we are able to model chaotic and nonchaotic time series. Furthermore, one critical point in modeling time series is the determination of the dimension of the embedding vector used, i.e., the number of components of the past that are needed to predict the future. With this method we can detect the embedding dimension by extracting the influence of the past on the future, i.e., the correlation of remote past and future
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems.
Kuptsov, Pavel V; Kuznetsov, Sergey P
2016-07-01
We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting, and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them, previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos. PMID:27575062
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems
Kuptsov, Pavel V.; Kuznetsov, Sergey P.
2016-01-01
We develop the numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes the computation of angle distribution between expanding, contracting and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them previously predicted hyperbolicity is confirmed. The third one provides an example of time-delay system with non-hyperbolic chaos.
Chaotic Scattering and Escape Times of Marginally Trapped Ultracold Neutrons
Coakley, K. J.; Doyle, J. M.; Dzhosyuk, S. N.; Yang, L.; Huffman, P. R.
2005-01-01
We compute classical trajectories of Ultracold neutrons (UCNs) in a superconducting Ioffe-type magnetic trap using a symplectic integration method. We find that the computed escape time for a particular set of initial conditions (momentum and position) does not generally stabilize as the time step parameter is reduced unless the escape time is short (less than approximately 10 s). For energy intervals where more than half of the escape times computed for UCN realizations are numerically well determined, we predict the median escape time as a function of the midpoint of the interval.
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.
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.
Sliding-Mode Synchronization Control for Uncertain Fractional-Order Chaotic Systems with Time Delay
Directory of Open Access Journals (Sweden)
Haorui Liu
2015-06-01
Full Text Available Specifically setting a time delay fractional financial system as the study object, this paper proposes a single controller method to eliminate the impact of model uncertainty and external disturbances on the system. The proposed method is based on the stability theory of Lyapunov sliding-mode adaptive control and fractional-order linear systems. The controller can fit the system state within the sliding-mode surface so as to realize synchronization of fractional-order chaotic systems. Analysis results demonstrate that the proposed single integral, sliding-mode control method can control the time delay fractional power system to realize chaotic synchronization, with strong robustness to external disturbance. The controller is simple in structure. The proposed method was also validated by numerical simulation.
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In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Directory of Open Access Journals (Sweden)
Cristian Rodriguez Rivero
2016-03-01
Full Text Available A new predictor algorithm based on Bayesian enhanced approach (BEA for long-term chaotic time series using artificial neural networks (ANN is presented. The technique based on stochastic models uses Bayesian inference by means of Fractional Brownian Motion as model data and Beta model as prior information. However, the need of experimental data for specifying and estimating causal models has not changed. Indeed, Bayes method provides another way to incorporate prior knowledge in forecasting models; the simplest representations of prior knowledge in forecasting models are hard to beat in many forecasting situations, either because prior knowledge is insufficient to improve on models or because prior knowledge leads to the conclusion that the situation is stable. This work contributes with long-term time series prediction, to give forecast horizons up to 18 steps ahead. Thus, the forecasted values and validation data are presented by solutions of benchmark chaotic series such as Mackey-Glass, Lorenz, Henon, Logistic, Rössler, Ikeda, Quadratic one-dimensional map series and monthly cumulative rainfall collected from Despeñaderos, Cordoba, Argentina. The computational results are evaluated against several non-linear ANN predictors proposed before on high roughness series that shows a better performance of Bayesian Enhanced approach in long-term forecasting.
Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel, E-mail: marcel.novaes@gmail.com
2015-10-15
We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.
Lag-generalized synchronization of time-delay chaotic systems with stochastic perturbation
Zhang, Shuo; Yu, Yongguang; Wen, Guoguang; Rahmani, Ahmed
2016-01-01
The lag-generalized synchronization of coupled time-delay chaotic systems with unknown parameters and stochastic perturbation is investigated. Based on the LaSalle-type invariance principle of stochastic differential equation, the synchronization is realized by analyzing stochastic stability of the error system. In order to achieve the synchronization, the unknown parameter update laws and the control laws are proposed. At last, two numerical examples are presented to show the effectiveness of the obtained theoretical results.
Discrete-Time Chaotic Circuits for Implementation of Tent Map and Bernoulli Map
Institute of Scientific and Technical Information of China (English)
LI Zhi-zhong; QIU Shui-sheng
2005-01-01
Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current (SI) techniques are presented. The two circuits can be constructed with 16MOSFET's and 2 capacitors. The simulations and experiments built with commercially available IC's for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.
Detecting Dynamical States from Noisy Time Series using Bicoherence
George, Sandip V; Misra, R
2016-01-01
Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information about the underlying nonlinearity from noisy time series. We show that a system evolving in the presence of noise which has its dynamical state concealed from quantifiers like the power spectrum and correlation dimension D2, can be revealed using the bicoherence function. We define an index called main peak bicoherence function as the bicoherence associated with the maximal power spectral peak. We show that this index is extremely useful while dealing with quasi-periodic data as it can distinguish strange non chaos from quasi periodicity even with added noise. We demonstrate this in a real world scenario, by taking the bicoherence of variable stars showing period doubling and strange non-chaotic behavior. Our results indicate that bicoherence analysis can also bypass the me...
A Chaotic Block Cipher for Real-Time Multimedia
M. Venkatesulu; N.Radha
2012-01-01
Problem statement: The widespread use of image, audio and video data makes media content protection increasingly necessary and important. We propose a naive approach which treats the multimedia signal to be protected as a text and use proposed encryption design to encrypt the whole data stream. Upon reception, the entire cipher text data stream would be decrypted and playback can be performed at the client end with an initial time delay. Approach: We introduce a block cipher algorithm, which ...
Detecting dynamical complexity changes in time series using the base-scale entropy
Institute of Scientific and Technical Information of China (English)
Li Jin; Ning Xin-Bao; Wu Wei; Ma Xiao-Fei
2005-01-01
Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series: the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.
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...
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.
The Foundations of Modern Time Series Analysis
Mills, Professor 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.
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...
Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control
International Nuclear Information System (INIS)
This paper studies delay-dependent stability of time-delay chaotic systems via time-delayed feedback control (DFC). The delay-dependent stability criteria via DFC are derived from the results based on standard feedback control (SFC), the method can be obtained to stabilize the system to an unstable fixed point. A numerical example is discussed to illustrate the advantage of the obtained result
Cherrier, Estelle; M'Saad, Mohammed; Farza, Mondher
2010-01-01
This work investigates high gain observer design to synchronize a time-delay chaotic system. It is shown that the underlying class of nonlinear systems can be put into the canonical observable form, and thus high gain observer design framework can be extended to chaotic synchronization problem. Our approach is motivated by its simplicity of implementation: the observer gain synthesis relies on the explicit resolution of a time-invariant algebraic Lyapunov equation, which leads to a single par...
Cherrier, Estelle; M'Saad, Mohammed
2009-01-01
This work investigates high gain observer design to synchronize a time-delay chaotic system. It is shown that the underlying class of nonlinear systems can be put into the canonical observable form, and thus high gain observer design framework can be extended to chaotic synchronization problem. Our approach is motivated by its simplicity of implementation: the observer gain synthesis relies on the explicit resolution of a time-invariant algebraic Lyapunov equation, which leads to a single par...
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results. PMID:25148672
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
International Nuclear Information System (INIS)
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches
Comparing entropy with tests for randomness as a measure of complexity in time series
Gan, Chee Chun
2015-01-01
Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a time series e.g. heartbeat. Ideally, entropy should be able to quantify the complexity of any underlying structure in the series, as well as determine if the variation arises from a random process. Unfortunately current entropy measures mostly are unable to perform the latter differentiation. Thus, a high entropy score indicates a random or chaotic series, whereas a low score indicates a high degree of regularity. This leads to the observation that current entropy measures are equivalent to evaluating how random a series is, or conversely the degree of regularity in a time series. This raises the possibility that existing tests for randomness, such as the runs test or permutation test, may have similar utility in diagnosing certain conditions. This paper compares various t...
Homogenising time series: beliefs, dogmas and facts
Domonkos, P.
2011-06-01
In the recent decades various homogenisation methods have been developed, but the real effects of their application on time series are still not known sufficiently. The ongoing COST action HOME (COST ES0601) is devoted to reveal the real impacts of homogenisation methods more detailed and with higher confidence than earlier. As a part of the COST activity, a benchmark dataset was built whose characteristics approach well the characteristics of real networks of observed time series. This dataset offers much better opportunity than ever before to test the wide variety of homogenisation methods, and analyse the real effects of selected theoretical recommendations. Empirical results show that real observed time series usually include several inhomogeneities of different sizes. Small inhomogeneities often have similar statistical characteristics than natural changes caused by climatic variability, thus the pure application of the classic theory that change-points of observed time series can be found and corrected one-by-one is impossible. However, after homogenisation the linear trends, seasonal changes and long-term fluctuations of time series are usually much closer to the reality than in raw time series. Some problems around detecting multiple structures of inhomogeneities, as well as that of time series comparisons within homogenisation procedures are discussed briefly in the study.
Searching of Chaotic Elements in Hydrology
Directory of Open Access Journals (Sweden)
Sorin VLAD
2014-03-01
Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.
Testing Mean Stability of Heteroskedastic Time Series
Violetta Dalla; Liudas Giraitis; Phillips, Peter C. B.
2015-01-01
Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of indepen...
Testing mean stability of heteroskedastic time series
Dalla, Violetta; Giraitis, Liudas; Phillips, Peter C. B.
2015-01-01
Time series models are often fitted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and financial data, particularly over long periods. Ignoring such shifts may result in fitting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the effects of unanticipated shocks. In spite of what may seem as obvious differences between a time series of indepen...
Time Series Analysis Using Composite Multiscale Entropy
Kung-Yen Lee; Chun-Chieh Wang; Shiou-Gwo Lin; Chiu-Wen Wu; Shuen-De Wu
2013-01-01
Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. S...
International Nuclear Information System (INIS)
Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach. (general)
Lee, Chaohong; Shi, Lei; Zhu, Xiwen; Gao, Kelin; Hai, Wenhua; Duan, Yiwu; Liu, Wing-Ki
2000-01-01
We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary conditio...
Institute of Scientific and Technical Information of China (English)
Wu Wei; Cui Bao-Tong
2007-01-01
In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented.This class of chaotic neural networks covers several well-known neural network, such a Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.
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
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
Visibility Graph Based Time Series Analysis.
Directory of Open Access Journals (Sweden)
Mutua Stephen
Full Text Available 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.
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
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.
Complex network approach to fractional time series
International Nuclear Information System (INIS)
In order to extract correlation information inherited in 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 fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as 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 anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series
Advanced spectral methods for climatic time series
Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.
2002-01-01
The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.
Complex network approach to fractional time series
Manshour, Pouya
2015-10-01
In order to extract correlation information inherited in 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 fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as 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 anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.
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.
Detecting nonlinear structure in time series
International Nuclear Information System (INIS)
We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a 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. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs
Indian Academy of Sciences (India)
Arturo C Martí; Marcelo Ponce; Cristina Masoller
2008-06-01
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the elements of the network are identical ( logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling strengths are uniform throughout the network. We show that if the delay times are su±ciently heterogeneous, for adequate coupling strength the network synchronizes in a spatially homogeneous steady state, which is unstable for the individual maps without coupling. This synchronization behavior is referred to as `suppression of chaos by random delays' and is in contrast with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently heterogeneous the synchronization behavior is largely independent of the network topology but depends on the network's connectivity, i.e., on the average number of neighbors per node.
Bayes linear variance adjustment for time series
Wilkinson, Darren J
2008-01-01
This paper exhibits quadratic products of linear combinations of observables which identify the covariance structure underlying the univariate locally linear time series dynamic linear model. The first- and second-order moments for the joint distribution over these observables are given, allowing Bayes linear learning for the underlying covariance structure for the time series model. An example is given which illustrates the methodology and highlights the practical implications of the theory.
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.
Nonlinear time series: semiparametric and nonparametric methods
Gao, Jiti
2007-01-01
Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully nonparametric models and methods. Answering the call for an up-to-date overview of the latest developments in the field, "Nonlinear Time Series: S...
International Nuclear Information System (INIS)
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
H∞ synchronization of chaotic neural networks with time-varying delays
International Nuclear Information System (INIS)
In this paper, we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov—Krasovskii functional and using a reciprocally convex approach, a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method
A constructional method for generalized synchronization of coupled time-delay chaotic systems
International Nuclear Information System (INIS)
A constructional method for detecting the existence and determining the functional relationship of generalized synchronization is introduced in this paper. Based on the stability theory of fixed points of dynamical systems, we show theoretically and numerically that an appropriate coupling scheme allows us to find the synchronization functional relationship between the states of coupled time-delay chaotic systems. On the other hand, given a synchronization function, this approach may help us to design the coupling scheme. To demonstrate the proposed method, Ikeda system is presented as an example.
Pseudo-periodic surrogate test to sample time series in stochastic softening Duffing oscillator
International Nuclear Information System (INIS)
Identification of typical noise-contaminated sample response is a hard task in a nonlinear system under stochastic background since irregularity of the sample response may come from measure noise, dynamical noise, or nonlinear effect, etc., and conventional dynamical methods are generally not useful. Here, the pseudo-periodic surrogate algorithm by Small is employed to test the sample time series in the softening Duffing oscillator under the Gaussian white noise excitation. The correlation dimensions of the noisy periodic and the noise-induced chaotic time series of the system are compared with those of their corresponding surrogate data respectively, the leading Lyapunov exponents by Rosenstein's algorithm are also presented for comparison
Institute of Scientific and Technical Information of China (English)
冯存芳; 汪映海
2011-01-01
Projective synchronization in modulated time-delayed systems is studied by applying an active control method. Based on the Lyapunov asymptotical stability theorem, the controller and sufficient condition for projective synchronization are calculated analytically. We give a genera./ method with which we can achieve projective synchronization in modulated time-delayed chaotic systems. This method allows us to adjust the desired scaling factor arbitrarily. The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices. Numerical simulations fully support the analytical approach.%Projective synchronization in modulated time-delayed systems is studied by applying an active control method.Based on the Lyapunov asymptotical stability theorem,the controller and sufficient condition for projective synchronization are calculated analytically.We give a general method with which we can achieve projective synchronization in modulated time-delayed chaotic systems.This method allows us to adjust the desired scaling factor arbitrarily.The effectiveness of our method is confirmed by using the famous delay-differential equations related to optical bistable or hybrid optical bistable devices.Numerical simulations fully support the analytical approach.
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.
Time series irreversibility: a visibility graph approach
Lacasa, Lucas; Roldán, Édgar; Parrondo, Juan M R; Luque, Bartolo
2011-01-01
We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (di...
Multiscale entropy analysis of electroseismic time series
L. Guzmán-Vargas; Ramírez-Rojas, A.; Angulo-Brown, F.
2008-01-01
In this work we use the multiscale entropy method to analyse the variability of geo-electric time series monitored in two sites located in Mexico. In our analysis we consider a period of time from January 1995 to December 1995. We systematically calculate the sample entropy of electroseismic time series. Important differences in the entropy profile for several time scales are observed in records from the same station. In particular, a complex behaviour is observed in the vicinity of a
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.
Testing time symmetry in time series using data compression dictionaries
Kennel, Matthew B.
2004-01-01
Time symmetry, often called statistical time reversibility, in a dynamical process means that any segment of time-series output has the same probability of occurrence in the process as its time reversal. A technique, based on symbolic dynamics, is proposed to distinguish such symmetrical processes from asymmetrical ones, given a time-series observation of the otherwise unknown process. Because linear stochastic Gaussian processes, and static nonlinear transformations of them, are statisticall...
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...
Analysis of Rattleback Chaotic Oscillations
Directory of Open Access Journals (Sweden)
Michael Hanias
2014-01-01
Full Text Available Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors’ invariant parameters.
Analysis of rattleback chaotic oscillations.
Hanias, Michael; Stavrinides, Stavros G; Banerjee, Santo
2014-01-01
Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback's chaotic dynamics are studied by applying Kane's model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors' invariant parameters. PMID:24511290
Energy Technology Data Exchange (ETDEWEB)
Schlick, Conor P., E-mail: conorschlick2015@u.northwestern.edu [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208 (United States); Umbanhowar, Paul B. [Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Ottino, Julio M. [Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208 (United States); Lueptow, Richard M., E-mail: r-lueptow@northwestern.edu [Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208 (United States); The Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, Illinois 60208 (United States)
2014-03-15
We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.
Area-preserving maps models of gyro-averaged ${\\bf E} \\times {\\bf B}$ chaotic transport
da Fonseca, J D; Caldas, I L
2014-01-01
Discrete maps have been extensively used to model 2-dimensional chaotic transport in plasmas and fluids. Here we focus on area-preserving maps describing finite Larmor radius (FLR) effects on ${\\bf E} \\times {\\bf B}$ chaotic transport in magnetized plasmas with zonal flows perturbed by electrostatic drift waves. FLR effects are included by gyro-averaging the Hamiltonians of the maps which, depending on the zonal flow profile, can have monotonic or non-monotonic frequencies. In the limit of zero Larmor radius, the monotonic frequency map reduces to the standard Chirikov-Taylor map, and, in the case of non-monotonic frequency, the map reduces to the standard nontwist map. We show that in both cases FLR leads to chaos suppression, changes in the stability of fixed points, and robustness of transport barriers. FLR effects are also responsible for changes in the phase space topology and zonal flow bifurcations. Dynamical systems methods based on recurrence time statistics are used to quantify the dependence on the...
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
Fractal and natural time analysis of geoelectrical time series
Ramirez Rojas, A.; Moreno-Torres, L. R.; Cervantes, F.
2013-05-01
In this work we show the analysis of geoelectric time series linked with two earthquakes of M=6.6 and M=7.4. That time series were monitored at the South Pacific Mexican coast, which is the most important active seismic subduction zone in México. The geolectric time series were analyzed by using two complementary methods: a fractal analysis, by means of the detrended fluctuation analysis (DFA) in the conventional time, and the power spectrum defined in natural time domain (NTD). In conventional time we found long-range correlations prior to the EQ-occurrences and simultaneously in NTD, the behavior of the power spectrum suggest the possible existence of seismo electric signals (SES) similar with the previously reported in equivalent time series monitored in Greece prior to earthquakes of relevant magnitude.
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. PMID:25751882
Climate Time Series Analysis and Forecasting
Young, P. C.; Fildes, R.
2009-04-01
This paper will discuss various aspects of climate time series data analysis, modelling and forecasting being carried out at Lancaster. This will include state-dependent parameter, nonlinear, stochastic modelling of globally averaged atmospheric carbon dioxide; the computation of emission strategies based on modern control theory; and extrapolative time series benchmark forecasts of annual average temperature, both global and local. The key to the forecasting evaluation will be the iterative estimation of forecast error based on rolling origin comparisons, as recommended in the forecasting research literature. The presentation will conclude with with a comparison of the time series forecasts with forecasts produced from global circulation models and a discussion of the implications for climate modelling research.
CALENDAR EFFECTS IN MONTHLY TIME SERIES MODELS
Institute of Scientific and Technical Information of China (English)
Gerhard THURY; Mi ZHOU
2005-01-01
It is not unusual for the level of a monthly economic time series, such as industrial production,retail and wholesale sales, monetary aggregates, telephone calls or road accidents, to be influenced by calendar effects. Such effects arise when changes occur in the level of activity resulting from differences in the composition of calendar between years. The two main sources of calendar effects are trading day variations and moving festivals. Ignoring such calendar effects will lead to substantial distortions in the identification stage of time series modeling. Therefore, it is mandatory to introduce calendar effects, when they are present in a time series, as the component of the model which one wants to estimate.
Chaotic Dynamics of Comet 1P/Halley; Lyapunov Exponent and Survival Time Expectancy
Muñoz-Gutiérrez, M A; Pichardo, B
2014-01-01
The orbital elements of comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit of comet Halley and to quantify the timescale over which its motion can be predicted confidently. In addition, we attempt to determine the timescale over which its present day orbit will remain stable. Numerical simulations of the dynamics of test particles in orbits similar to that of comet Halley are carried out with the Mercury 6.2 code. On the basis of these we construct survival time maps to assess the absolute stability of Halley's orbit, frequency analysis maps, to study the variability of the orbit and we calculate the Lyapunov exponent for the orbit for variations in initial conditions at the level of the present day uncertainties in our knowledge of its orbital parameters. On the basis of our calculations of the Lyapunov exponent for comet Halley, the chaotic nat...
Spending too much time at the Galactic bar: chaotic fanning of the Ophiuchus stream
Price-Whelan, Adrian M; Johnston, Kathryn V; Rix, Hans-Walter
2016-01-01
The Ophiuchus stellar stream is peculiar: (1) its length is short given the age of its constituent stars, and (2) several probable member stars that lie close in both sky position and velocity have dispersions in these dimensions that far exceed those seen within the stream. The stream's proximity to the Galactic center suggests that the bar must have a significant influence on its dynamical history: The triaxiality and time-dependence of the bar may generate chaotic orbits in the vicinity of the stream that can greatly affect its morphology. We explore this hypothesis with models of stream formation along orbits consistent with Ophiuchus' properties in a Milky Way potential model that includes a rotating bar. We find that in all choices for the rotation parameters of the bar, orbits fit to the stream are strongly chaotic. Mock streams generated along these orbits qualitatively match the observed properties of the stream: because of chaos, stars stripped early generally form low-density, high-dispersion "fans...
Fuzzy Information Granules in Time Series Data
HEIKO HOFER; ORTOLANI M; DAVID PATTERSON; FRANK HOEPPNER; ONDINE CALLAN; Berthold, Michael R
2004-01-01
Often, it is desirable to represent a set of time series through typical shapes in order to detect common patterns. The algorithm presented here compares pieces of a different time series in order to find such similar shapes. The use of a fuzzy clustering technique based on fuzzy c-means allows us to detect shapes that belong to a certain group of typical shapes with a degree of membership. Modifications to the original algorithm also allow this matching to be invariant with respect to a scal...
Case study in time series analysis
Zhongjie, Xie
1993-01-01
This book is a monograph on case studies using time series analysis, which includes the main research works applied to practical projects by the author in the past 15 years. The works cover different problems in broad fields, such as: engineering, labour protection, astronomy, physiology, endocrinology, oil development, etc. The first part of this book introduces some basic knowledge of time series analysis which is necessary for the reader to understand the methods and the theory used in the procedure for solving problems. The second part is the main part of this book - case studies in differ
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, ...
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.
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...
The distribution of "time of flight" in 3D stationary chaotic advection
Raynal, Florence
2014-01-01
The distributions of "time of flight" (time spent by a single fluid particle between two crossings of the Poincar\\'e section) are investigated for five different 3D stationary chaotic mixers. Above all, we study the large tails of those distributions, and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically dfferent, with a very large tail following a power law with an exponent close to -3.
The distribution of “time of flight” in three dimensional stationary chaotic advection
Energy Technology Data Exchange (ETDEWEB)
Raynal, Florence; Carrière, Philippe [LMFA, UMR CNRS–Université de Lyon, École Centrale de Lyon–Université Lyon 1–INSA Lyon, École Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Écully cédex (France)
2015-04-15
The distributions of “time of flight” (time spent by a single fluid particle between two crossings of the Poincaré section) are investigated for five different three dimensional stationary chaotic mixers. Above all, we study the large tails of those distributions and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically different, with a very large tail following a power law with an exponent close to −3.
Exploring sensitive dependence and transitivity to optimize travel time in chaotic systems
International Nuclear Information System (INIS)
Transitivity and sensitive dependence on initial conditions are the main characteristics of chaotic behavior. The latter one can be exploited so that small controlled perturbations in system parameters may imply a faster transfer in time from a desired start point to a neighborhood of a desired final state. In this study three targeting approaches are evaluated: The first one uses a geometric approach to find the proper perturbation which allows a faster transfer between two desired points; The second, an evolutionary algorithm called GEO (Generalized External Optimization), is adapted to search for optimized orbits; The third one, uses successive perturbations along the path in order to direct the orbits to the final desired point in a short time interval. These three methods are evaluated regarding performance and implementation complexity
The distribution of “time of flight” in three dimensional stationary chaotic advection
International Nuclear Information System (INIS)
The distributions of “time of flight” (time spent by a single fluid particle between two crossings of the Poincaré section) are investigated for five different three dimensional stationary chaotic mixers. Above all, we study the large tails of those distributions and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically different, with a very large tail following a power law with an exponent close to −3
Time series tapering for short data samples
DEFF Research Database (Denmark)
Kaimal, J.C.; Kristensen, L.
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. The Ha...
Asymptotic spectral theory for nonlinear time series
Shao, Xiaofeng; Wu, Wei Biao
2007-01-01
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.
On Bayesian Nonparametric Continuous Time Series Models
Karabatsos, George; Walker, Stephen G.
2013-01-01
This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it turns out, the model is well known in multiple change-point problems.
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.
Nonlinear time-series analysis revisited.
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data-typically univariate-via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems. PMID:26428563
Inferring causality from noisy time series data
DEFF Research Database (Denmark)
Mønster, Dan; Fusaroli, Riccardo; Tylén, Kristian;
2016-01-01
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...
Nonlinear time-series analysis revisited
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data—typically univariate—via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems.
Multiscale entropy analysis of electroseismic time series
Directory of Open Access Journals (Sweden)
L. Guzmán-Vargas
2008-08-01
Full Text Available In this work we use the multiscale entropy method to analyse the variability of geo-electric time series monitored in two sites located in Mexico. In our analysis we consider a period of time from January 1995 to December 1995. We systematically calculate the sample entropy of electroseismic time series. Important differences in the entropy profile for several time scales are observed in records from the same station. In particular, a complex behaviour is observed in the vicinity of a M=7.4 EQ occurred on 14 September 1995. Besides, we also compare the changes in the entropy of the original data with their corresponding shuffled version.
Time Series Analysis Using Composite Multiscale Entropy
Directory of Open Access Journals (Sweden)
Kung-Yen Lee
2013-03-01
Full Text Available Multiscale entropy (MSE was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE is introduced to overcome this difficulty. Simulation results on both white noise and 1/f noise show that the CMSE provides higher entropy reliablity than the MSE approach for large time scale factors. On real data analysis, both the MSE and CMSE are applied to extract features from fault bearing vibration signals. Experimental results demonstrate that the proposed CMSE-based feature extractor provides higher separability than the MSE-based feature extractor.
Fractal Analysis On Internet Traffic Time Series
Chong, K B
2002-01-01
Fractal behavior and long-range dependence have been observed in tele-traffic measurement and characterization. In this paper we show results of application of the fractal analysis to internet traffic via various methods. Our result demonstrate that the internet traffic exhibits self-similarity. Time-scale analysis show to be an effective way to characterize the local irregularity. Based on the result of this study, these two Internet time series exhibit fractal characteristic with long-range dependence.
Time series regression studies in environmental epidemiology
Bhaskaran, Krishnan; Gasparrini, Antonio; Hajat, Shakoor; Smeeth, Liam; Armstrong, Ben
2013-01-01
Time series regression studies have been widely used in environmental epidemiology, notably in investigating the short-term associations between exposures such as air pollution, weather variables or pollen, and health outcomes such as mortality, myocardial infarction or disease-specific hospital admissions. Typically, for both exposure and outcome, data are available at regular time intervals (e.g. daily pollution levels and daily mortality counts) and the aim is to explore short-term associa...
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.
Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control
Directory of Open Access Journals (Sweden)
Feng-Hsiag Hsiao
2013-01-01
Full Text Available This study presents an effective approach to realize the optimal exponential synchronization of multiple time-delay chaotic (MTDC systems. First, a neural network (NN model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov’s direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI. Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work.
Time series regression studies in environmental epidemiology.
Bhaskaran, Krishnan; Gasparrini, Antonio; Hajat, Shakoor; Smeeth, Liam; Armstrong, Ben
2013-08-01
Time series regression studies have been widely used in environmental epidemiology, notably in investigating the short-term associations between exposures such as air pollution, weather variables or pollen, and health outcomes such as mortality, myocardial infarction or disease-specific hospital admissions. Typically, for both exposure and outcome, data are available at regular time intervals (e.g. daily pollution levels and daily mortality counts) and the aim is to explore short-term associations between them. In this article, we describe the general features of time series data, and we outline the analysis process, beginning with descriptive analysis, then focusing on issues in time series regression that differ from other regression methods: modelling short-term fluctuations in the presence of seasonal and long-term patterns, dealing with time varying confounding factors and modelling delayed ('lagged') associations between exposure and outcome. We finish with advice on model checking and sensitivity analysis, and some common extensions to the basic model. PMID:23760528
International Nuclear Information System (INIS)
To quantitatively evaluate the time-delay (TD) signatures of chaotic signals generated by vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated optical feedback (PROF), we propose four cases of resolution coefficients R based on correlation functions. The resolution coefficient characteristics for the x-polarization (XP) mode, y-polarization (YP) mode and the total output are considered. The dependences of R on the feedback strength and feedback delay are discussed and compared carefully. The two-dimensional maps of R show that the TD signatures for the single polarization mode (i.e., XP or YP mode) are much more difficult to retrieve than those for the total output in the entire parameter space. Thus, by using single polarization mode as a chaotic carrier, the TD signatures are extremely difficult to be identified, which contributes a lot in the security-enhanced VCSELs-based chaotic optical communication systems. (fundamental areas of phenomenology (including applications))
International Nuclear Information System (INIS)
This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur'e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur'e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi–perturbation chaotic Lur'e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method. (general)
Ma, Tie-Dong; Zhang, Hua-Guang; Fu, Jie
2008-12-01
This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur'e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur'e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur'e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.
Research on the Prediction of VNN Neural Network Traffic Flow Model Based on Chaotic Algorithm
Directory of Open Access Journals (Sweden)
Yin Lisheng
2013-06-01
Full Text Available This paperresearches on the prediction of traffic flow chaotic time series based on VNNTF neural network. First, the traffic flow time series chaotic feature is extracted by chaos theory. Pretreatment for traffic flow time series and the VNNTP neural networks model was build by this. Second, principles of neural network learning algorithm VNNTF is described. Based on chaotic learning algorithm, the neural network traffic Volterra learning algorithm isdesigned for fast learning algorithm. Last, a single-step prediction of traffic flow chaotic time series is researched by VNNTF network model based on chaotic algorithm. The results showed that the VNNTF network model predictive performance is better than the Volterra prediction filter and the BP neural network by the simulation results and root-mean-square value.
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.
Altmann, Eduardo G; Tél, Tamás
2015-01-01
We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.
Time Series Analysis Using Geometric Template Matching.
Frank, Jordan; Mannor, Shie; Pineau, Joelle; Precup, Doina
2013-03-01
We present a novel framework for analyzing univariate time series data. At the heart of the approach is a versatile algorithm for measuring the similarity of two segments of time series called geometric template matching (GeTeM). First, we use GeTeM to compute a similarity measure for clustering and nearest-neighbor classification. Next, we present a semi-supervised learning algorithm that uses the similarity measure with hierarchical clustering in order to improve classification performance when unlabeled training data are available. Finally, we present a boosting framework called TDEBOOST, which uses an ensemble of GeTeM classifiers. TDEBOOST augments the traditional boosting approach with an additional step in which the features used as inputs to the classifier are adapted at each step to improve the training error. We empirically evaluate the proposed approaches on several datasets, such as accelerometer data collected from wearable sensors and ECG data. PMID:22641699
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.
Spending Too Much Time at the Galactic Bar: Chaotic Fanning of the Ophiuchus Stream
Price-Whelan, Adrian M.; Sesar, Branimir; Johnston, Kathryn V.; Rix, Hans-Walter
2016-06-01
The Ophiuchus stellar stream is peculiar: (1) its length is short given the age of its constituent stars, and (2) several probable member stars have dispersions in sky position and velocity that far exceed those seen within the stream. The stream’s proximity to the Galactic center suggests that its dynamical history is significantly influenced by the Galactic bar. We explore this hypothesis with models of stream formation along orbits consistent with Ophiuchus’ properties in a Milky Way potential model that includes a rotating bar. In all choices for the rotation parameters of the bar, orbits fit to the stream are strongly chaotic. Mock streams generated along these orbits qualitatively match the observed properties of the stream: because of chaos, stars stripped early generally form low-density, high-dispersion “fans” leaving only the most recently disrupted material detectable as a strong over-density. Our models predict that there should be a significant amount of low-surface-brightness tidal debris around the stream with a complex phase-space morphology. The existence of or lack of these features could provide interesting constraints on the Milky Way bar and would rule out formation scenarios for the stream. This is the first time that chaos has been used to explain the properties of a stellar stream and is the first demonstration of the dynamical importance of chaos in the Galactic halo. The existence of long, thin streams around the Milky Way, presumably formed along non- or weakly chaotic orbits, may represent only a subset of the total population of disrupted satellites.
International Nuclear Information System (INIS)
In this Letter, two adaptive controllers are proposed for the lag-synchronization of two non-identical time-delayed chaotic systems with fully unknown parameters. Based on Lyapunov-stability theorem and adaptive techniques, sufficient conditions for the lag-synchronization of these two systems are discussed. Finally, illustrative examples are given to verify the validity of the developed controllers.
Multivariate Voronoi Outlier Detection for Time Series
Zwilling, Chris E.; Wang, Michelle Yongmei
2014-01-01
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 d...
Estimation and Forecasting in Time Series Models
Zhang, Ru
2013-01-01
This dissertation covers several topics in estimation and forecasting in time series models. Chapter one is about estimation and feasible conditional forecasts properties from the predictive regressions, which extends previous results of OLS estimation bias in the predictive regression model by considering predictive regressions with possible zero intercepts, and also allowing the regressor to follow either a stationary AR(1) process or unit root process. The main thrust of this chapter is t...
Bayes analysis of time series with covariates
Czech Academy of Sciences Publication Activity Database
Volf, Petr
Hradec Králové : Gaudeamus, 2005 - (Skalská, H.), s. 421-426 ISBN 978-80-7041-535-1. [Mathematical Methods in Economics 2005 /23./. Hradec Králové (CZ), 14.09.2005-16.09.2005] R&D Projects: GA ČR GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayes analysis * time series * unemployment data Subject RIV: BB - Applied Statistics, Operational Research
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.
Applying time series analysis to performance logs
Kubacki, Marcin; Sosnowski, Janusz
2015-09-01
Contemporary computer systems provide mechanisms for monitoring various performance parameters (e.g. processor or memory usage, disc or network transfers), which are collected and stored in performance logs. An important issue is to derive characteristic features describing normal and abnormal behavior of the systems. For this purpose we use various schemes of analyzing time series. They have been adapted to the specificity of performance logs and verified using data collected from real systems. The presented approach is useful in evaluating system dependability.
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 not...... 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....
Time-series models in marketing.
Dekimpe, Marnik; Hanssens, DM
2000-01-01
Leeflang and Wittink (2000) identify three past stages in marketing model building and implementation, review the current status, and provide some intriguing thoughts on how the model-building process may evolve in response to ongoing and anticipated developments in the marketing environment. It is interesting to note that time-series techniques are not mentioned in their review of the past, receive considerable attention in their assessment of the current situation (mainly in the context of ...
Nonparametric inference for unbalance time series data
Oliver Linton
2004-01-01
Estimation of heteroskedasticity and autocorrelation consistent covariance matrices (HACs) is a well established problem in time series. Results have been established under a variety of weak conditions on temporal dependence and heterogeneity that allow one to conduct inference on a variety of statistics, see Newey and West (1987), Hansen (1992), de Jong and Davidson (2000), and Robinson (2004). Indeed there is an extensive literature on automating these procedures starting with Andrews (1991...
Nonparametric inference for unbalanced time series data
Linton, Oliver Bruce
2004-01-01
Estimation of heteroskedasticity and autocorrelation consistent covariance matrices (HACs) is a well established problem in time series. Results have been established under a variety of weak conditions on temporal dependence and heterogeneity that allow one to conduct inference on a variety of statistics, see Newey and West (1987), Hansen (1992), de Jong and Davidson (2000), and Robinson (2004). Indeed there is an extensive literature on automating these procedures starting with Andrews (1991...
Evolving time series forecasting ARMA models
Cortez, Paulo; Rocha, Miguel
2004-01-01
Nowadays, the ability to forecast the future, based only on past data, leads to strategic advantages, which may be the key to success in organizations. Time Series Forecasting (TSF) allows the modeling of complex systems as ``black-boxes'', being a focus of attention in several research arenas such as Operational Research, Statistics or Computer Science. Alternative TSF approaches emerged from the Artificial Intelligence arena, where optimization algorithms inspired on natural selection pr...
Time Series Forecasting with Missing Values
Shin-Fu Wu; Chia-Yung Chang; Shie-Jue Lee
2015-01-01
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, o...
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
Analysis of Polyphonic Musical Time Series
Sommer, Katrin; Weihs, Claus
A general model for pitch tracking of polyphonic musical time series will be introduced. Based on a model of Davy and Godsill (Bayesian harmonic models for musical pitch estimation and analysis, Technical Report 431, Cambridge University Engineering Department, 2002) Davy and Godsill (2002) the different pitches of the musical sound are estimated with MCMC methods simultaneously. Additionally a preprocessing step is designed to improve the estimation of the fundamental frequencies (A comparative study on polyphonic musical time series using MCMC methods. In C. Preisach et al., editors, Data Analysis, Machine Learning, and Applications, Springer, Berlin, 2008). The preprocessing step compares real audio data with an alphabet constructed from the McGill Master Samples (Opolko and Wapnick, McGill University Master Samples [Compact disc], McGill University, Montreal, 1987) and consists of tones of different instruments. The tones with minimal Itakura-Saito distortion (Gray et al., Transactions on Acoustics, Speech, and Signal Processing ASSP-28(4):367-376, 1980) are chosen as first estimates and as starting points for the MCMC algorithms. Furthermore the implementation of the alphabet is an approach for the recognition of the instruments generating the musical time series. Results are presented for mixed monophonic data from McGill and for self recorded polyphonic audio data.
Nonlinear time-series analysis of current signal in cathodic contact glow discharge electrolysis
Allagui, Anis; Rojas, Andrea Espinel; Bonny, Talal; Elwakil, Ahmed S.; Abdelkareem, Mohammad Ali
2016-05-01
In the standard two-electrode configuration employed in electrolytic process, when the control dc voltage is brought to a critical value, the system undergoes a transition from conventional electrolysis to contact glow discharge electrolysis (CGDE), which has also been referred to as liquid-submerged micro-plasma, glow discharge plasma electrolysis, electrode effect, electrolytic plasma, etc. The light-emitting process is associated with the development of an irregular and erratic current time-series which has been arbitrarily labelled as "random," and thus dissuaded further research in this direction. Here, we examine the current time-series signals measured in cathodic CGDE configuration in a concentrated KOH solution at different dc bias voltages greater than the critical voltage. We show that the signals are, in fact, not random according to the NIST SP. 800-22 test suite definition. We also demonstrate that post-processing low-pass filtered sequences requires less time than the native as-measured sequences, suggesting a superposition of low frequency chaotic fluctuations and high frequency behaviors (which may be produced by more than one possible source of entropy). Using an array of nonlinear time-series analyses for dynamical systems, i.e., the computation of largest Lyapunov exponents and correlation dimensions, and re-construction of phase portraits, we found that low-pass filtered datasets undergo a transition from quasi-periodic to chaotic to quasi-hyper-chaotic behavior, and back again to chaos when the voltage controlling-parameter is increased. The high frequency part of the signals is discussed in terms of highly nonlinear turbulent motion developed around the working electrode.
Nonlinear time series analysis of the fluctuations of the geomagnetic horizontal field
Directory of Open Access Journals (Sweden)
B. George
Full Text Available A detailed nonlinear time series analysis of the hourly data of the geomagnetic horizontal intensity H measured at Kodaikanal (10.2° N; 77.5° E; mag: dip 3.5° N has been carried out to investigate the dynamical behaviour of the fluctuations of H. The recurrence plots, spatiotemporal entropy and the result of the surrogate data test show the deterministic nature of the fluctuations, rejecting the hypothesis that H belong to the family of linear stochastic signals. The low dimensional character of the dynamics is evident from the estimated value of the correlation dimension and the fraction of false neighbours calculated for various embedding dimensions. The exponential decay of the power spectrum and the positive Lyapunov exponent indicate chaotic behaviour of the underlying dynamics of H. This is also supported by the results of the comparison of the chaotic characteristics of the time series of H with the pseudo-chaotic characteristics of coloured noise time series. We have also shown that the error involved in the short-term prediction of successive values of H, using a simple but robust, zero-order nonlinear prediction method, increases exponentially. It has also been suggested that there exists the possibility of characterizing the geomagnetic fluctuations in terms of the invariants in chaos theory, such as Lyapunov exponents and correlation dimension. The results of the analysis could also have implications in the development of a suitable model for the daily fluctuations of geomagnetic horizontal intensity.
Key words. Geomagnetism and paleomagnetism (time variations, diurnal to secular – History of geophysics (solar-planetary relationships Magnetospheric physics (storms and substorms
Time Series Forecasting: A Multivariate Stochastic Approach
Sello, Stefano
1999-01-01
This note deals with a multivariate stochastic approach to forecast the behaviour of a cyclic time series. Particular attention is devoted to the problem of the prediction of time behaviour of sunspot numbers for the current 23th cycle. The idea is to consider the previous known n cycles as n particular realizations of a given stochastic process. The aim is to predict the future behaviour of the current n+1th realization given a portion of the curve and the structure of the previous n realiza...
Fuzzy model-based adaptive synchronization of time-delayed chaotic systems
International Nuclear Information System (INIS)
In this paper, fuzzy model-based synchronization of a class of first order chaotic systems described by delayed-differential equations is addressed. To design the fuzzy controller, the chaotic system is modeled by Takagi-Sugeno fuzzy system considering the properties of the nonlinear part of the system. Assuming that the parameters of the chaotic system are unknown, an adaptive law is derived to estimate these unknown parameters, and the stability of error dynamics is guaranteed by Lyapunov theory. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.
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 ...
Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA
International Nuclear Information System (INIS)
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake. SSA and PCA are used to study the long time-scale characteristics of the time series. MFDFA is applied for investigating all time scales up to the smallest recorded one. It turns out that the majority of the long time-scale dynamics, that is presumably dominated by the structural dynamics of the brake system, is dominated by very few active dimensions only and can well be understood in terms of low dimensional chaotic attractors. The multi-fractal analysis shows that the fast dynamical processes originating in the friction interface are in turn truly multi-scale in nature
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.
Increasing-order Projective Synchronization of Chaotic Systems with Time Delay
Institute of Scientific and Technical Information of China (English)
MIAO Qing-Ying; FANG Jian-An; TANG Yang; DONG Ai-Hua
2009-01-01
This work is concerned with lag projective synchronization of chaotic systems with increasing order. The systems under consideration have unknown parameters and different structures. Combining the adaptive control method and feedback control technique, we design a suitable controller and parameter update law to achieve lag synchronization of chaotic systems with increasing order. The result is rigorously proved by the Lyapunov stability theorem. Moreover, corresponding simulation results are given to verify the effectiveness of the proposed methods.
Increasing-order Projective Synchronization of Chaotic Systems with Time Delay
International Nuclear Information System (INIS)
This work is concerned with lag projective synchronization of chaotic systems with increasing order. The systems under consideration have unknown parameters and different structures. Combining the adaptive control method and feedback control technique, we design a suitable controller and parameter update law to achieve lag synchronization of chaotic systems with increasing order. The result is rigorously proved by the Lyapunov stability theorem. Moreover, corresponding simulation results are given to verify the effectiveness of the proposed methods. (general)
Energy Technology Data Exchange (ETDEWEB)
Cui Baotong [School of Communication and Control Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China)], E-mail: btcui@vip.sohu.com; Lou Xuyang [School of Communication and Control Engineering, Southern Yangtze University, 1800 Lihu Road, Wuxi, Jiangsu 214122 (China)], E-mail: louxuyang28945@163.com
2009-01-15
In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.
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
In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model a......- ular case where the data-generating process is a simple artificial neural network model. Suggestions for further reading conclude the paper....... 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...
Measuring the distance between time series
Moeckel, Richard; Murray, Brad
1997-02-01
To evaluate models of dynamical systems, researchers have traditionally used quantitative measures of short term prediction errors. However, for chaotic or stochastic systems, comparison of long term, qualitative behaviors may be more relevant. Let x = ( x0,…, xn) be a sequence of real numbers generated by sampling a dynamical system or stochastic process and suppose y = ( y0,…, yn) is another sequence, generated by a mathematical model of the process which generated x. In this paper we consider several ways of assigning a distance d( x, y) which measures the difference in long term behavior.
Generation and control of multi-scroll chaotic attractors in fractional order systems
International Nuclear Information System (INIS)
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations
Time series analysis of temporal networks
Sikdar, Sandipan; Ganguly, Niloy; Mukherjee, Animesh
2016-01-01
A common but an important feature of all real-world networks is that they are temporal in nature, i.e., the network structure changes over time. Due to this dynamic nature, it becomes difficult to propose suitable growth models that can explain the various important characteristic properties of these networks. In fact, in many application oriented studies only knowing these properties is sufficient. For instance, if one wishes to launch a targeted attack on a network, this can be done even without the knowledge of the full network structure; rather an estimate of some of the properties is sufficient enough to launch the attack. We, in this paper show that even if the network structure at a future time point is not available one can still manage to estimate its properties. We propose a novel method to map a temporal network to a set of time series instances, analyze them and using a standard forecast model of time series, try to predict the properties of a temporal network at a later time instance. To our aim, we consider eight properties such as number of active nodes, average degree, clustering coefficient etc. and apply our prediction framework on them. We mainly focus on the temporal network of human face-to-face contacts and observe that it represents a stochastic process with memory that can be modeled as Auto-Regressive-Integrated-Moving-Average (ARIMA). We use cross validation techniques to find the percentage accuracy of our predictions. An important observation is that the frequency domain properties of the time series obtained from spectrogram analysis could be used to refine the prediction framework by identifying beforehand the cases where the error in prediction is likely to be high. This leads to an improvement of 7.96% (for error level ≤20%) in prediction accuracy on an average across all datasets. As an application we show how such prediction scheme can be used to launch targeted attacks on temporal networks. Contribution to the Topical Issue
Time series modelling of surface pressure data
Al-Awadhi, Shafeeqah; Jolliffe, Ian
1998-03-01
In this paper we examine time series modelling of surface pressure data, as measured by a barograph, at Herne Bay, England, during the years 1981-1989. Autoregressive moving average (ARMA) models have been popular in many fields over the past 20 years, although applications in climatology have been rather less widespread than in some disciplines. Some recent examples are Milionis and Davies (Int. J. Climatol., 14, 569-579) and Seleshi et al. (Int. J. Climatol., 14, 911-923). We fit standard ARMA models to the pressure data separately for each of six 2-month natural seasons. Differences between the best fitting models for different seasons are discussed. Barograph data are recorded continuously, whereas ARMA models are fitted to discretely recorded data. The effect of different spacings between the fitted data on the models chosen is discussed briefly.Often, ARMA models can give a parsimonious and interpretable representation of a time series, but for many series the assumptions underlying such models are not fully satisfied, and more complex models may be considered. A specific feature of surface pressure data in the UK is that its behaviour is different at high and at low pressures: day-to-day changes are typically larger at low pressure levels than at higher levels. This means that standard assumptions used in fitting ARMA models are not valid, and two ways of overcoming this problem are investigated. Transformation of the data to better satisfy the usual assumptions is considered, as is the use of non-linear, specifically threshold autoregressive (TAR), models.
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.
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.
International Nuclear Information System (INIS)
We propose an interpolation formula for the distribution of the reflection coefficient in the presence of time reversal symmetry for chaotic cavities with absorption. This is done assuming a similar functional form as when time reversal invariance is absent. The interpolation formula reduces to the analytical expressions for the strong and weak absorption limits. Our proposal is compared to the quite complicated exact result existing in the literature
ANALYSIS AND APPLIED STUDY OF DYNAMIC CHARACTERISTICS OF CHAOTIC REPELLER IN COMPLICATED SYSTEM
Institute of Scientific and Technical Information of China (English)
MA Jun-hai; REN Biao; CHEN Yu-shu
2005-01-01
Fractal characters and fractal dimension of time series created by repeller in complicated system were studied and the time series were reconstructed by applying the theory of phase space reconstruction for chaotic time series. The influence of zero-mean treatment, Fourier filter on prediction for time series were studied. The choice of prediction sample affects the relative error and the prediction length which were also under good concern. The results show that the model provided here are practical for the modeling and prediction of time series created by chaotic repellers. Zero-mean treatment has changed prediction result quantitatively for chaotic repeller sample data. But using Fourier filter may decrease the prediction precision. This is theoretical and practical for study on chaotic repeller in complicated system.
Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal
Indian Academy of Sciences (India)
Thomas Kuruvilla; V M Nandakumaran
2000-03-01
The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.
Radhakrishnan, Srinivasan; Duvvuru, Arjun; Sultornsanee, Sivarit; Kamarthi, Sagar
2016-02-01
The cross correlation coefficient has been widely applied in financial time series analysis, in specific, for understanding chaotic behaviour in terms of stock price and index movements during crisis periods. To better understand time series correlation dynamics, the cross correlation matrices are represented as networks, in which a node stands for an individual time series and a link indicates cross correlation between a pair of nodes. These networks are converted into simpler trees using different schemes. In this context, Minimum Spanning Trees (MST) are the most favoured tree structures because of their ability to preserve all the nodes and thereby retain essential information imbued in the network. Although cross correlations underlying MSTs capture essential information, they do not faithfully capture dynamic behaviour embedded in the time series data of financial systems because cross correlation is a reliable measure only if the relationship between the time series is linear. To address the issue, this work investigates a new measure called phase synchronization (PS) for establishing correlations among different time series which relate to one another, linearly or nonlinearly. In this approach the strength of a link between a pair of time series (nodes) is determined by the level of phase synchronization between them. We compare the performance of phase synchronization based MST with cross correlation based MST along selected network measures across temporal frame that includes economically good and crisis periods. We observe agreement in the directionality of the results across these two methods. They show similar trends, upward or downward, when comparing selected network measures. Though both the methods give similar trends, the phase synchronization based MST is a more reliable representation of the dynamic behaviour of financial systems than the cross correlation based MST because of the former's ability to quantify nonlinear relationships among time
Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability
Li, Chunlai; Zhang, Jing
2016-07-01
The issue of synchronisation for a fractional-order chaotic system with uncertainties and disturbance is studied in this paper. The finite-time input-to-state stable theory of fractional-order dynamical system is presented for the first time. A linear feedback controller is proposed to achieve synchronisation of this fractional-order system and guarantee the bounded state error for any bounded interference in finite time. Since the chaotic system displays special dynamical behaviours as invariable Lyapunov exponent spectrums and controllable signal amplitude, one can achieve complete synchronisation and projective synchronisation by only adjusting the system parameter. Numerical simulations are shown to verify the feasibility of the presented synchronisation scheme.
The role of a delay time on the spatial structure of chaotically advected reactive scalars
Tzella, Alexandra
2009-01-01
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\\"older exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length s...
Directory of Open Access Journals (Sweden)
Guo-Jheng Yang
2013-08-01
Full Text Available The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on the Internet are digital, protection has become a critical issue, and determining how to use digital watermarks to protect digital media is thus the topic of our research. This paper uses the Logistic map with parameter u = 4 to generate chaotic dynamic behavior with the maximum entropy 1. This approach increases the security and rigor of the protection. The main research target of information hiding is determining how to hide confidential data so that the naked eye cannot see the difference. Next, we introduce one method of information hiding. Generally speaking, if the image only goes through Arnold’s cat map and the Logistic map, it seems to lack sufficient security. Therefore, our emphasis is on controlling Arnold’s cat map and the initial value of the chaos system to undergo small changes and generate different chaos sequences. Thus, the current time is used to not only make encryption more stringent but also to enhance the security of the digital media.
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.
Periodograms for Multiband Astronomical Time Series
VanderPlas, Jacob T
2015-01-01
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. We use simulated light curves and randomly subsampled SDSS Stripe 82 data to demonstrate the superiority...
Load Forecasting Using Time Series Models
Directory of Open Access Journals (Sweden)
Mahendran Shitan
2009-09-01
Full Text Available Load forecasting is a process of predicting the future load demands. It is important for power systemplanners and demand controllers in ensuring that there would be enough generation to cope withthe increasing demand. Accurate model for load forecasting can lead to a better budget planning,maintenance scheduling and fuel management. This paper presents an attempt to forecast the maximumdemand of electricity by finding an appropriate time series model. The methods considered in this studyinclude the Naïve method, Exponential smoothing, Seasonal Holt-Winters, ARMA, ARAR algorithm, andRegression with ARMA Errors. The performance of these different methods was evaluated by using theforecasting accuracy criteria namely, the Mean Absolute Error (MAE, Root Mean Square Error (RMSE andMean Absolute Relative Percentage Error (MARPE. Based on these three criteria the pure autoregressivemodel with an order 2, or AR (2 under ARMA family emerged as the best model for forecasting electricitydemand.
Correlation filtering in financial time series
Aste, T; Tumminello, M; Mantegna, R N
2005-01-01
We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al. \\cite{TumminielloPNAS05}, we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).
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.
Chaotic strings in a near Penrose limit of AdS$_5\\times T^{1,1}$
Asano, Yuhma; Kyono, Hideki; Yoshida, Kentaroh
2015-01-01
We study chaotic motions of a classical string in a near Penrose limit of AdS$_5\\times T^{1,1}$. It is known that chaotic solutions appear on $R\\times T^{1,1}$, depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable speratrix, so that chaotic motions are generated as a consequence of collapsed Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then we provide a support for the existence of chaos by computing Poincar\\'e sections. In comparison to the AdS$_5\\times T^{1,1}$ case, we argue that no chaos lives in a near Penrose limit of AdS$_5\\times$S$^5$ as expected from the classical integrability of the parent system.
Cervantes, F.; Gonzalez, J.; Real, C.; Hoyos, L.
2012-12-01
ABSTRACT: Chaotic invariants like fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. In this work four fractal dimension estimation algorithms are applied to non-linear time series. The algorithms employed are the Higuchi's algorithm, the Petrosian's algorithm, the Katz's Algorithm and the Box counting method. The analyzed time series are associated with natural phenomena, the Dst a geomagnetic index which monitors the world wide magnetic storm; the Dst index is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a behavior self-similar, which depend on the time scale of measurements. It is also observed that fractal dimensions may not be constant over all time scales.
Institute of Scientific and Technical Information of China (English)
Gong Li-Hua; Zhou Nan-Run; Hu Li-Yun; Fan Hong-Yi
2012-01-01
A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented.The new differential equation for determining the parameter of the density operator p(t) is derived and the solution of f' for the damping and gaining processes are studied separately.Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.
Shahverdiev, E. M.; Shore, K. A.
2009-01-01
We present the first report of the synchronization regimes in both unidirectionally and bidirectionally-coupled multiple time delay chaotic laser diodes subject to incoherent optical feedbacks and incoherent optical injection. We derive the existence conditions and numerically study the stability for lag, complete, and anticipating synchronization regimes and cascaded synchronization. We also study in detail the effect of parameter mismatches and noise on the synchronization quality. It is em...
Time series predictions with neural nets: Application to airborne pollen forecasting
Arizmendi, C. M.; Sanchez, J. R.; Ramos, N. E.; Ramos, G. I.
1993-09-01
Pollen allergy is a common disease causing rhinoconjunctivitis (hay fever) in 5 10% of the population. Medical studies have indicated that pollen related diseases could be highly reduced if future pollen contents in the air could be predicted. In this work we have developed a new forecasting method that applies the ability of neural nets to predict the future behaviour of chaotic systems in order to make accurate predictions of the airborne pollen concentration. The method requires that the neural net be fed with non-zero values, which restricts the method predictions to the period following the start of pollen flight. The operational method outlined here constitutes a different point of view with respect to the more generally used forecasts of time series analysis, which require input of many meteorological parameters. Excellent forecasts were obtained training a neural net by using only the time series pollen concentration values.
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.
Time series models with a common stochastic variance for analysing economic time series
Koopman, S.J.; C.S. Bos
2002-01-01
This discussion paper led to an article in Statistica Neerlandica (2003). Vol. 57, issue 4, pages 439-469. The linear Gaussian state space model for which the common variance istreated as a stochastic time-varying variable is considered for themodelling of economic time series. The focus of this paper is on thesimultaneous estimation of parameters related to the stochasticprocesses of the mean part and the variance part of the model. Theestimation method is based on maximum likelihood and it ...
Fractal dimension algorithms and their application to time series associated with natural phenomena
International Nuclear Information System (INIS)
Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed
Directory of Open Access Journals (Sweden)
Xiaomin Xu
2015-11-01
Full Text Available The uncertainty and regularity of wind power generation are caused by wind resources’ intermittent and randomness. Such volatility brings severe challenges to the wind power grid. The requirements for ultrashort-term and short-term wind power forecasting with high prediction accuracy of the model used, have great significance for reducing the phenomenon of abandoned wind power , optimizing the conventional power generation plan, adjusting the maintenance schedule and developing real-time monitoring systems. Therefore, accurate forecasting of wind power generation is important in electric load forecasting. The echo state network (ESN is a new recurrent neural network composed of input, hidden layer and output layers. It can approximate well the nonlinear system and achieves great results in nonlinear chaotic time series forecasting. Besides, the ESN is simpler and less computationally demanding than the traditional neural network training, which provides more accurate training results. Aiming at addressing the disadvantages of standard ESN, this paper has made some improvements. Combined with the complementary advantages of particle swarm optimization and tabu search, the generalization of ESN is improved. To verify the validity and applicability of this method, case studies of multitime scale forecasting of wind power output are carried out to reconstruct the chaotic time series of the actual wind power generation data in a certain region to predict wind power generation. Meanwhile, the influence of seasonal factors on wind power is taken into consideration. Compared with the classical ESN and the conventional Back Propagation (BP neural network, the results verify the superiority of the proposed method.
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
An improved harmony search algorithm for synchronization of discrete-time chaotic systems
International Nuclear Information System (INIS)
The harmony search (HS) algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. HS was conceptualized using an analogy with music improvisation process where music players improvise the pitches of their instruments to obtain better harmony. The HS algorithm does not require initial values and uses a random search instead of a gradient search, so derivative information is unnecessary. Furthermore, the HS algorithm is simple in concept, few in parameters, easy in implementation, imposes fewer mathematical requirements, and does not require initial value settings of the decision variables. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The tuning of a proportional-integral-derivative (PID) controller based on an improved HS (IHS) algorithm for synchronization of two identical discrete chaotic systems subject the different initial conditions is investigated in this paper. Simulation results of the IHS to determine the PID parameters to synchronization of two Henon chaotic systems are compared with other HS approaches including classical HS and global-best HS. Numerical results reveal that the proposed IHS method is a powerful search and controller design optimization tool for synchronization of chaotic systems.
Peat conditions mapping using MODIS time series
Poggio, Laura; Gimona, Alessandro; Bruneau, Patricia; Johnson, Sally; McBride, Andrew; Artz, Rebekka
2016-04-01
Large areas of Scotland are covered in peatlands, providing an important sink of carbon in their near natural state but act as a potential source of gaseous and dissolved carbon emission if not in good conditions. Data on the condition of most peatlands in Scotland are, however, scarce and largely confined to sites under nature protection designations, often biased towards sites in better condition. The best information available at present is derived from labour intensive field-based monitoring of relatively few designated sites (Common Standard Monitoring Dataset). In order to provide a national dataset of peat conditions, the available point information from the CSM data was modelled with morphological features and information derived from MODIS sensor. In particular we used time series of indices describing vegetation greenness (Enhanced Vegetation Index), water availability (Normalised Water Difference index), Land Surface Temperature and vegetation productivity (Gross Primary productivity). A scorpan-kriging approach was used, in particular using Generalised Additive Models for the description of the trend. The model provided the probability of a site to be in favourable conditions and the uncertainty of the predictions was taken into account. The internal validation (leave-one-out) provided a mis-classification error of around 0.25. The derived dataset was then used, among others, in the decision making process for the selection of sites for restoration.
Machado, Rubens E G
2016-01-01
Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic models, fully incorporating the time-dependent nature of the systems. Here we aim at analysing the fractions of chaotic motion within different morphological components of the galaxy. We wish to investigate how the presence of chaotic orbits evolves with time, and how their spatial distribution is associated with morphological features of the galaxy. We employ a time-dependent analytical potential model that was derived from an N-body simulation of a strongly barred galaxy. With this analytical potential we may follow the dynamical evolution of ensembles of orbits. Using the Generalized Alignment Index (GALI) chaos detection method, we study the fraction of chaotic orbits, sampling the dynamics of both the stellar disc and of the dark matter halo. Within the stellar disc, th...
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...
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...
Some results of analysis of source position time series
Malkin, Zinovy
2015-01-01
Source position time series produced by International VLBI Service for Geodesy and astrometry (IVS) Analysis Centers were analyzed. These series was computed using different software and analysis strategy. Comparison of this series showed that they have considerably different scatter and systematic behavior. Based on the inspection of all the series, new sources were identified as sources with irregular (non-random) position variations. Two statistics used to estimate the noise level in the time series, namely RMS and ADEV were compared.
Deflation-based separation of uncorrelated stationary time series
Miettinen, Jari; Nordhausen, Klaus; Oja, Hannu; Taskinen, Sara
2014-01-01
In this paper we assume that the observed pp time series are linear combinations of pp latent uncorrelated weakly stationary time series. The problem is then to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure t...
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...
Correlation control theory of chaotic laser systems
International Nuclear Information System (INIS)
A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)
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.
The role of a delay time on the spatial structure of chaotically advected reactive scalars
Tzella, Alexandra; Haynes, Peter H.
2009-01-01
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\\"older exponent that depends on th...
Notes on time serie analysis, ARIMA models and signal extraction
Kaiser, Regina; Maravall, Agustín
2000-01-01
Present practice in applied time series work, mostly at economic policy or data producing agencies, relies heavily on using moving average filters to estimate unobserved components (or signals) in time series, such as the seasonally adjusted series, the trend, or the cycle. The purpose of the present paper is to provide an informal introduction to the time series analysis tools and concepts required by the user or analyst to understand the basic methodology behind the application of filters. ...
Driscoll, T; Pershin, Y. V.; Basov, D. N.; Di Ventra, M.
2011-01-01
We suggest and experimentally demonstrate a chaotic memory resistor (memristor). The core of our approach is to use a resistive system whose equations of motion for its internal state variables are similar to those describing a particle in a multi-well potential. Using a memristor emulator, the chaotic memristor is realized and its chaotic properties are measured. A Poincar\\'{e} plot showing chaos is presented for a simple nonautonomous circuit involving only a voltage source directly connect...
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.
Stability of operation versus temperature of a three-phase clock-driven chaotic circuit
International Nuclear Information System (INIS)
We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal—oxide—semiconductor (MOS) chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis (SPICE) using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided. (general)
Outlier Detection in Structural Time Series Models
DEFF Research Database (Denmark)
Marczak, Martyna; Proietti, Tommaso
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–to–sp...
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...
Mellor, Vincent
2011-01-01
This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common methods, including global and local polynomial fitting, are discussed in terms of their applicability, level of computation and accuracy. One example method, Measure based Reconstruction, has been investigated in greater detail and experimentation is carried out to evaluate the method. In this project we shall be looking at the different ways one can model chaotic time series. The reason we are going to look at a range of methods is that different methods are "good" for different applications. As the "goodness" of a model is subjective to the task one wishes to do, we will investigate a selected models and compare the prediction to see how one goes about testing a model.
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.
International Nuclear Information System (INIS)
We study different types of projective synchronization (projective-anticipating, projective, and projective-lag synchronization) in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor α can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of α. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model. (general)
Vyhnalek, Brian; Zurcher, Ulrich; O'Dwyer, Rebecca; Kaufman, Miron
2009-10-01
A wide range of heart rate irregularities have been reported in small studies of patients with temporal lobe epilepsy [TLE]. We hypothesize that patients with TLE display cardiac dysautonomia in either a subclinical or clinical manner. In a small study, we have retrospectively identified (2003-8) two groups of patients from the epilepsy monitoring unit [EMU] at the Cleveland Clinic. No patients were diagnosed with cardiovascular morbidities. The control group consisted of patients with confirmed pseudoseizures and the experimental group had confirmed right temporal lobe epilepsy through a seizure free outcome after temporal lobectomy. We quantified the heart rate variability using the approximate entropy [ApEn]. We found similar values of the ApEn in all three states of consciousness (awake, sleep, and proceeding seizure onset). In the TLE group, there is some evidence for greater variability in the awake than in either the sleep or proceeding seizure onset. Here we present results for mathematically-generated time series: the heart rate fluctuations ξ follow the γ statistics i.e., p(ξ)=γ-1(k) ξ^k exp(-ξ). This probability function has well-known properties and its Shannon entropy can be expressed in terms of the γ-function. The parameter k allows us to generate a family of heart rate time series with different statistics. The ApEn calculated for the generated time series for different values of k mimic the properties found for the TLE and pseudoseizure group. Our results suggest that the ApEn is an effective tool to probe differences in statistics of heart rate fluctuations.
Multiscale entropy to distinguish physiologic and synthetic RR time series.
Costa, M; Goldberger, A L; Peng, C-K
2002-01-01
We address the challenge of distinguishing physiologic interbeat interval time series from those generated by synthetic algorithms via a newly developed multiscale entropy method. Traditional measures of time series complexity only quantify the degree of regularity on a single time scale. However, many physiologic variables, such as heart rate, fluctuate in a very complex manner and present correlations over multiple time scales. We have proposed a new method to calculate multiscale entropy from complex signals. In order to distinguish between physiologic and synthetic time series, we first applied the method to a learning set of RR time series derived from healthy subjects. We empirically established selected criteria characterizing the entropy dependence on scale factor for these datasets. We then applied this algorithm to the CinC 2002 test datasets. Using only the multiscale entropy method, we correctly classified 48 of 50 (96%) time series. In combination with Fourier spectral analysis, we correctly classified all time series. PMID:14686448
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.
Identifying timescales and possible precursors of the awake to asleep transition in EOG time series
International Nuclear Information System (INIS)
In this work we study the awake to asleep state transition in eye blinking activity. In this perspective the human electroculographic activity (EOG) was first experimentally investigated by means of a spectral analyses of the time series resulting for processes underlying both the brain activity and the eye dynamics. We studied the evolution of the spectral content both via the classical spectrogram and with the computation of summarizing scalar parameters: mean frequency, maximum frequency, spectral variance. With these tools we highlighted a significative dynamical change appearing before the transition from the awake to the asleep state, characterized by a general widening of the spectrum, that translates into a decrease of the maximum frequency, an increase of the average frequency and an increase of the spectral variance. Due to inherently high non-linearities involved, chaotic patterns were likely to occur in the experimental time series. These were analyzed therefore with the chaos theory. In particular we studied the time evolution of dynamical parameters as computed on different windows of the time series, i.e. optimal delay time as suggested by autocorrelation and mutual information on one side, embedding quality evaluation as suggested by the False Nearest Neighbours percentage on the other
Identification of chaotic systems with hidden variables (modified Bock's algorithm)
International Nuclear Information System (INIS)
We address the problem of estimating parameters of chaotic dynamical systems from a time series in a situation when some of state variables are not observed and/or the data are very noisy. Using specially developed quantitative criteria, we compare performance of the original multiple shooting approach (Bock's algorithm) and its modified version. The latter is shown to be significantly superior for long chaotic time series. In particular, it allows to obtain accurate estimates for much worse starting guesses for the estimated parameters
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.
Multifractal Analysis of Aging and Complexity in Heartbeat Time Series
Muñoz D., Alejandro; Almanza V., Victor H.; del Río C., José L.
2004-09-01
Recently multifractal analysis has been used intensively in the analysis of physiological time series. In this work we apply the multifractal analysis to the study of heartbeat time series from healthy young subjects and other series obtained from old healthy subjects. We show that this multifractal formalism could be a useful tool to discriminate these two kinds of series. We used the algorithm proposed by Chhabra and Jensen that provides a highly accurate, practical and efficient method for the direct computation of the singularity spectrum. Aging causes loss of multifractality in the heartbeat time series, it means that heartbeat time series of elderly persons are less complex than the time series of young persons. This analysis reveals a new level of complexity characterized by the wide range of necessary exponents to characterize the dynamics of young people.
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.
Visibility graph network analysis of gold price time series
Long, Yu
2013-08-01
Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L∼lnN into lnL∼lnN as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.
Directory of Open Access Journals (Sweden)
Wentao Mao
2015-01-01
Full Text Available Accurate and fast prediction of nonstationary time series is challenging and of great interest in both practical and academic areas. In this paper, an online sequential extreme learning machine with new weighted strategy is proposed for nonstationary time series prediction. First, a new leave-one-out (LOO cross-validation error estimation for online sequential data is proposed based on inversion of block matrix. Second, a new weighted strategy based on the proposed LOO error estimation is proposed. This strategy ranks the samples’ importance by means of the LOO error of each new added sample and then assigns various weights. Performance comparisons of the proposed method with other existing algorithms are presented based on chaotic and real-world nonstationary time series data. The results show that the proposed method outperforms the classical ELM and OS-ELM in terms of generalization performance and numerical stability.
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 ...
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 ...
Power-weighted densities for time series data
McCarthy, Daniel M.; Jensen, Shane T.
2016-01-01
While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the parameters of a chosen time series model. In our power-weighted density (PWD) approach, observations in the distant past are down-weighted in the likelihood function relative to more recent observations, while still giving the practitioner control over the choice o...
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.
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,…
Experimental nonlinear dynamical studies in cesium magneto-optical trap using time-series analysis
Energy Technology Data Exchange (ETDEWEB)
Anwar, M., E-mail: mamalik2000@gmail.com; Islam, R.; Faisal, M. [National Institute of Lasers and Optronics, P.O. Nilore, Islamabad 44000, PK (Pakistan); Sikandar, M.; Ahmed, M. [Pakistan Institute of Engineering and Applied Sciences, P.O. Nilore, Islamabad 44000, PK (Pakistan)
2015-03-30
A magneto-optical trap of neutral atoms is essentially a dissipative quantum system. The fast thermal atoms continuously dissipate their energy to the environment via spontaneous emissions during the cooling. The atoms are, therefore, strongly coupled with the vacuum reservoir and the laser field. The vacuum fluctuations as well as the field fluctuations are imparted to the atoms as random photon recoils. Consequently, the external and internal dynamics of atoms becomes stochastic. In this paper, we have investigated the stochastic dynamics of the atoms in a magneto-optical trap during the loading process. The time series analysis of the fluorescence signal shows that the dynamics of the atoms evolves, like all dissipative systems, from deterministic to the chaotic regime. The subsequent disappearance and revival of chaos was attributed to chaos synchronization between spatially different atoms in the magneto-optical trap.
FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting
Directory of Open Access Journals (Sweden)
Miquel L. Alomar
2016-01-01
Full Text Available Hardware implementation of artificial neural networks (ANNs allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC has arisen as a strategic technique to design recurrent neural networks (RNNs with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. The proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement different arithmetic operations. The result is the development of a highly functional system with low hardware resources. The presented methodology is applied to chaotic time-series forecasting.
Experimental nonlinear dynamical studies in cesium magneto-optical trap using time-series analysis
International Nuclear Information System (INIS)
A magneto-optical trap of neutral atoms is essentially a dissipative quantum system. The fast thermal atoms continuously dissipate their energy to the environment via spontaneous emissions during the cooling. The atoms are, therefore, strongly coupled with the vacuum reservoir and the laser field. The vacuum fluctuations as well as the field fluctuations are imparted to the atoms as random photon recoils. Consequently, the external and internal dynamics of atoms becomes stochastic. In this paper, we have investigated the stochastic dynamics of the atoms in a magneto-optical trap during the loading process. The time series analysis of the fluorescence signal shows that the dynamics of the atoms evolves, like all dissipative systems, from deterministic to the chaotic regime. The subsequent disappearance and revival of chaos was attributed to chaos synchronization between spatially different atoms in the magneto-optical trap
Time Series Properties of Expectation Biases
Kinari, Yusuke
2011-01-01
This study exammes time senes properties of expectation biases usmg a highfrequency survey on stock price forecasts, which required participants to forecast the Nikkei 225 over three forecasting horizons: one day, one week, and one month ahead. Constructing proxies for overconfidence and optimism as the expectation biases, this study shows that overconfidence is likely to remain stable over time while optimism is not. Moreover, a relationship exists between optimism and stock price movement, ...
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. .
Volatility modeling of rainfall time series
Yusof, Fadhilah; Kane, Ibrahim Lawal
2013-07-01
Networks of rain gauges can provide a better insight into the spatial and temporal variability of rainfall, but they tend to be too widely spaced for accurate estimates. A way to estimate the spatial variability of rainfall between gauge points is to interpolate between them. This paper evaluates the spatial autocorrelation of rainfall data in some locations in Peninsular Malaysia using geostatistical technique. The results give an insight on the spatial variability of rainfall in the area, as such, two rain gauges were selected for an in-depth study of the temporal dependence of the rainfall data-generating process. It could be shown that rainfall data are affected by nonlinear characteristics of the variance often referred to as variance clustering or volatility, where large changes tend to follow large changes and small changes tend to follow small changes. The autocorrelation structure of the residuals and the squared residuals derived from autoregressive integrated moving average (ARIMA) models were inspected, the residuals are uncorrelated but the squared residuals show autocorrelation, and the Ljung-Box test confirmed the results. A test based on the Lagrange multiplier principle was applied to the squared residuals from the ARIMA models. The results of this auxiliary test show a clear evidence to reject the null hypothesis of no autoregressive conditional heteroskedasticity (ARCH) effect. Hence, it indicates that generalized ARCH (GARCH) modeling is necessary. An ARIMA error model is proposed to capture the mean behavior and a GARCH model for modeling heteroskedasticity (variance behavior) of the residuals from the ARIMA model. Therefore, the composite ARIMA-GARCH model captures the dynamics of daily rainfall in the study area. On the other hand, seasonal ARIMA model became a suitable model for the monthly average rainfall series of the same locations treated.
Fitting dynamic fator models to nonstationary time series
Eichler, M.; Motta, Giovanni; Von Sachs, Rainer
2008-01-01
Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure,i.e. allowing f...
Fitting dynamic factor models to non-stationary time series
Eichler Michael; Motta Giovanni; Sachs Rainer von
2009-01-01
Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infin...
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.
Chaotic Combustion in Spark Ignition Engines
Wendeker, M.; Czarnigowski, J.; Litak, G.; Szabelski, K.
2002-01-01
We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the observation of unperiodicity in the time series, suitable stroboscopic maps and a complex structure of a reconstructed strange attractor. This analysis can explain that in some circumstances the level of noise in spark ignition engines increases considerably due...
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
A Computer Evolution in Teaching Undergraduate Time Series
Hodgess, Erin M.
2004-01-01
In teaching undergraduate time series courses, we have used a mixture of various statistical packages. We have finally been able to teach all of the applied concepts within one statistical package; R. This article describes the process that we use to conduct a thorough analysis of a time series. An example with a data set is provided. We compare…
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.
Stata: The language of choice for time series analysis?
Christopher F. Baum
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.
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...
Using Time-Series Regression to Predict Academic Library Circulations.
Brooks, Terrence A.
1984-01-01
Four methods were used to forecast monthly circulation totals in 15 midwestern academic libraries: dummy time-series regression, lagged time-series regression, simple average (straight-line forecasting), monthly average (naive forecasting). In tests of forecasting accuracy, dummy regression method and monthly mean method exhibited smallest average…
Two Fractal Overlap Time Series: Earthquakes and Market Crashes
Chakrabarti, Bikas K.; Arnab Chatterjee; Pratip Bhattacharyya
2007-01-01
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.
Reprocessed height time series for GPS stations
S. Rudenko; Schön, N.; Uhlemann, M; G. Gendt
2013-01-01
Precise weekly positions of 403 Global Positioning System (GPS) stations located worldwide are obtained by reprocessing GPS data of these stations for the time span from 4 January 1998 until 29 December 2007. The processing algorithms and models used as well as the solution and results obtained are presented. Vertical velocities of 266 GPS stations having a tracking history longer than 2.5 yr are computed; 107 of them are GPS stations located at tide gauges (TIGA observing stations). The vert...
Chaotic time series prediction based on a novel robust echo state network.
Li, Decai; Han, Min; Wang, Jun
2012-05-01
In this paper, a robust recurrent neural network is presented in a Bayesian framework based on echo state mechanisms. Since the new model is capable of handling outliers in the training data set, it is termed as a robust echo state network (RESN). The RESN inherits the basic idea of ESN learning in a Bayesian framework, but replaces the commonly used Gaussian distribution with a Laplace one, which is more robust to outliers, as the likelihood function of the model output. Moreover, the training of the RESN is facilitated by employing a bound optimization algorithm, based on which, a proper surrogate function is derived and the Laplace likelihood function is approximated by a Gaussian one, while remaining robust to outliers. It leads to an efficient method for estimating model parameters, which can be solved by using a Bayesian evidence procedure in a fully autonomous way. Experimental results show that the proposed method is robust in the presence of outliers and is superior to existing methods. PMID:24806127
Using wavelets for time series forecasting: Does it pay off?
Schlüter, Stephan; Deuschle, Carola
2010-01-01
By means of wavelet transform a time series can be decomposed into a time dependent sum of frequency components. As a result we are able to capture seasonalities with time-varying period and intensity, which nourishes the belief that incorporating the wavelet transform in existing forecasting methods can improve their quality. The article aims to verify this by comparing the power of classical and wavelet based techniques on the basis of four time series, each of them having individual charac...
Time-Series Photometric Surveys: Some Musings
Howell, S. B.
We live in the era of large astronomical surveys aimed at collecting high photometric precision, high time resolution, and long term (near) continuous observations. Such surveys discover many variable sources and their study has led to new paradigms in observational astronomy. Periodic variables have a long and venerable history in astronomy being highly useful as distance ladders, to investigate stellar interior physics and to map out Galactic structure. However, typically less than 10% of all variable sources are periodic and a detailed understanding of the majority of variables, the non-periodic sources, is lacking. What can we learn from non-periodic variables? Are there alternative techniques or types of study that may help elucidate their true nature? This talk will attempt to provide a short review of our understanding of variable sources and provide some suggestions for a methodology toward the study of non-variable astronomical sources.
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......% 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...... a significant number of candlestick sequences whose output signals (measured against an unseen set of stocks) have predictive accuracy which varies between 60% and 95% depended on the type of pattern....
Interactive analysis of gappy bivariate time series using AGSS
Lewis, Peter A.W.; Ray, Bonnie K.
1992-01-01
Bivariate time series which display nonstationary behavior, such as cycles or long-term trends, are common in fields such as oceanography and meteorology. These are usually very large-scale data sets and often may contain long gaps of missing values in one or both series, with the gaps perhaps occurring at different time periods in the two series. We present a simplified but effective method of interactively examining and filling in the missing values in such series using extensions of the me...
Comparison of New and Old Sunspot Number Time Series
Cliver, E. W.
2016-06-01
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.
Application of p-adic analysis to time series
Khrennikov, A. Yu.; Kozyrev, S. V.; Oleschko, K. (collab.); Jaramillo, A. G.; Lopez, M. de Jesus Correa
2013-01-01
Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree--like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.
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.
Nonlinear time-series analysis of Hyperion's lightcurves
Tarnopolski, Mariusz
2014-01-01
Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be ...
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.
Database for Hydrological Time Series of Inland Waters (DAHITI)
Schwatke, Christian; Dettmering, Denise
2016-04-01
Satellite altimetry was designed for ocean applications. However, since some years, satellite altimetry is also used over inland water to estimate water level time series of lakes, rivers and wetlands. The resulting water level time series can help to understand the water cycle of system earth and makes altimetry to a very useful instrument for hydrological applications. In this poster, we introduce the "Database for Hydrological Time Series of Inland Waters" (DAHITI). Currently, the database contains about 350 water level time series of lakes, reservoirs, rivers, and wetlands which are freely available after a short registration process via http://dahiti.dgfi.tum.de. In this poster, we introduce the product of DAHITI and the functionality of the DAHITI web service. Furthermore, selected examples of inland water targets are presented in detail. DAHITI provides time series of water level heights of inland water bodies and their formal errors . These time series are available within the period of 1992-2015 and have varying temporal resolutions depending on the data coverage of the investigated water body. The accuracies of the water level time series depend mainly on the extent of the investigated water body and the quality of the altimeter measurements. Hereby, an external validation with in-situ data reveals RMS differences between 5 cm and 40 cm for lakes and 10 cm and 140 cm for rivers, respectively.
Piecewise Trend Approximation: A Ratio-Based Time Series Representation
Directory of Open Access Journals (Sweden)
Jingpei Dan
2013-01-01
Full Text Available A time series representation, piecewise trend approximation (PTA, is proposed to improve efficiency of time series data mining in high dimensional large databases. PTA represents time series in concise form while retaining main trends in original time series; the dimensionality of original data is therefore reduced, and the key features are maintained. Different from the representations that based on original data space, PTA transforms original data space into the feature space of ratio between any two consecutive data points in original time series, of which sign and magnitude indicate changing direction and degree of local trend, respectively. Based on the ratio-based feature space, segmentation is performed such that each two conjoint segments have different trends, and then the piecewise segments are approximated by the ratios between the first and last points within the segments. To validate the proposed PTA, it is compared with classical time series representations PAA and APCA on two classical datasets by applying the commonly used K-NN classification algorithm. For ControlChart dataset, PTA outperforms them by 3.55% and 2.33% higher classification accuracy and 8.94% and 7.07% higher for Mixed-BagShapes dataset, respectively. It is indicated that the proposed PTA is effective for high dimensional time series data mining.
Wei, Qing-Lai; Song, Rui-Zhuo; Sun, Qiu-Ye; Xiao, Wen-Dong
2015-09-01
This paper estimates an off-policy integral reinforcement learning (IRL) algorithm to obtain the optimal tracking control of unknown chaotic systems. Off-policy IRL can learn the solution of the HJB equation from the system data generated by an arbitrary control. Moreover, off-policy IRL can be regarded as a direct learning method, which avoids the identification of system dynamics. In this paper, the performance index function is first given based on the system tracking error and control error. For solving the Hamilton-Jacobi-Bellman (HJB) equation, an off-policy IRL algorithm is proposed. It is proven that the iterative control makes the tracking error system asymptotically stable, and the iterative performance index function is convergent. Simulation study demonstrates the effectiveness of the developed tracking control method. Project supported by the National Natural Science Foundation of China (Grant Nos. 61304079 and 61374105), the Beijing Natural Science Foundation, China (Grant Nos. 4132078 and 4143065), the China Postdoctoral Science Foundation (Grant No. 2013M530527), the Fundamental Research Funds for the Central Universities, China (Grant No. FRF-TP-14-119A2), and the Open Research Project from State Key Laboratory of Management and Control for Complex Systems, China (Grant No. 20150104).
Forecasting Compositional Time Series with Exponential Smoothing Methods
Anne B. Koehler; Ralph D Snyder; J Keith Ord; Adrian Beaumont
2010-01-01
Compositional time series are formed from measurements of proportions that sum to one in each period of time. We might be interested in forecasting the proportion of home loans that have adjustable rates, the proportion of nonagricultural jobs in manufacturing, the proportion of a rock's geochemical composition that is a specific oxide, or the proportion of an election betting market choosing a particular candidate. A problem may involve many related time series of proportions. There could be...
Image-Based Learning Approach Applied to Time Series Forecasting
J. C. Chimal-Eguía; K. Ramírez-Amáro
2012-01-01
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 data representation is based on information obtained by image axis division into boxes. The difference between this new input data representation and the classical is that this technique is not time-dependent. This new information is implemented in the new Image-Based Learning A...
Artificial neural networks applied to forecasting time series
Montaño Moreno, Juan José; Palmer Pol, Alfonso; Muñoz Gracia, María del Pilar
2011-01-01
This study offers a description and comparison of the main models of Artificial Neural Networks (ANN) which have proved to be useful in time series forecasting, and also a standard procedure for the practical application of ANN in this type of task. The Multilayer Perceptron (MLP), Radial Base Function (RBF), Generalized Regression Neural Network (GRNN), and Recurrent Neural Network (RNN) models are analyzed. With this aim in mind, we use a time series made up of 244 time points. A comparativ...
Analysis of multidimensional geophysical monitoring time series for earthquake prediction
Lyubushin, A. A.
1999-01-01
A method is presented for detection of synchronous signals in multidimensional time series data. It is based on estimation of eigenvalues of spectral matrices and canonical coherences in moving time windows and extraction of an aggregated signal (a scalar signal, which accumulates in its own variations only those spectral components which are present simultaneously in each scalar time series). It is known that an increase in the collective behavior of the components of some systems and an enl...
Investigating effects in GNSS station coordinate time series
Haritonova, Diana; Balodis, Janis; Janpaule, Inese
2014-01-01
The vertical and horizontal displacements of the Earth can be measured to a high degree of precision using GNSS. Time series of Latvian GNSS station positions of both the EUPOS®-Riga and LatPos networks have been developed at the Institute of Geodesy and Geoinformation of the University of Latvia (LU GGI). In this study the main focus is made on the noise analysis of the obtained time series and site displacement identification. The results of time series have been analysed and distinctive be...
Analysis of complex time series using refined composite multiscale entropy
Energy Technology Data Exchange (ETDEWEB)
Wu, Shuen-De; Wu, Chiu-Wen [Department of Mechatronic Technology, National Taiwan Normal University, Taipei 10610, Taiwan (China); Lin, Shiou-Gwo [Department of Communications, Navigation and Control Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan (China); Lee, Kung-Yen [Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei 10617, Taiwan (China); Peng, Chung-Kang [College of Health Sciences and Technology, National Central University, Chung-Li 32001, Taiwan (China); Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center/Harvard Medical School, Boston (United States)
2014-04-01
Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.
Estimation of connectivity measures in gappy time series
Papadopoulos, G
2015-01-01
A new method is proposed to compute connectivity measures on multivariate time series with gaps. Rather than removing or filling the gaps, the rows of the joint data matrix containing empty entries are removed and the calculations are done on the remainder matrix. The method, called measure adapted gap removal (MAGR), can be applied to any connectivity measure that uses a joint data matrix, such as cross correlation, cross mutual information and transfer entropy. MAGR is favorably compared using these three measures to a number of known gap-filling techniques, as well as the gap closure. The superiority of MAGR is illustrated on time series from synthetic systems and financial time series.
Segmentation of Nonstationary Time Series with Geometric Clustering
DEFF Research Database (Denmark)
Bocharov, Alexei; Thiesson, Bo
2013-01-01
We introduce a non-parametric method for segmentation in regimeswitching time-series models. The approach is based on spectral clustering of target-regressor tuples and derives a switching regression tree, where regime switches are modeled by oblique splits. Such models can be learned efficiently...... from data, where clustering is used to propose one single split candidate at each split level. We use the class of ART time series models to serve as illustration, but because of the non-parametric nature of our segmentation approach, it readily generalizes to a wide range of time-series models that go...
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
Are oil markets chaotic? A non-linear dynamic analysis
International Nuclear Information System (INIS)
The analysis of products' price behaviour continues to be an important empirical issue. This study contributes to the current literature on price dynamics of products by examining for the presence of chaos and non-linear dynamics in daily oil products for the Rotterdam and Mediterranean petroleum markets. Previous studies using only one invariant, such as the correlation dimension may not effectively determine the chaotic structure of the underlying time series. To obtain better information on the time series structure, a framework is developed, where both invariant and non-invariant quantities were also examined. In this paper various invariants for detecting a chaotic time series were analysed along with the associated Brock's theorem and Eckman-Ruelle condition, to return series for the prices of oil products. An additional non-invariant quantity, the BDS statistic, was also examined. The correlation dimension, entropies and Lyapunov exponents show strong evidence of chaos in a number of oil products considered. 30 refs
The chaotic marriage of physics and financial economics
Gilmore, Claire
2013-01-01
By the early 1980s interest in chaos theory was spreading from mathematics and the sciences to other fields, including economics and finance. Initial results, based on the metric approach to testing for chaos in time series data, appeared to lend support to the presence of chaotic behavior in a variety of economic phenomena and in financial markets. Subsequently, a topological approach to the analysis of chaos was developed which led to tests for chaotic behavior more suited to the relatively small, noisy data sets typically available in these fields. This close returns test is demonstrated here and is applied to data from several financial markets. The qualitative topological test does not support evidence of a chaotic generating mechanism in these series. The quantitative form of the close returns test indicates nonchaotic nonlinear behavior that cannot be fully explained by current financial models.
On chaotic graphs and applications in physics and biology
International Nuclear Information System (INIS)
El Naschie's ε ∞ theory in Quantum space time is given and discussed geometrically and topologically as a category of fuzzy spaces, these fuzzy categories in which lines are fuzzy fractal lines. In this paper, we represent the chaotic graphs as many fuzzy fractal lines up to ∞. We will describe them by chaotic matrices. Many fuzzy systems (chaotic systems) are. This article introduces some operations on the chaotic graphs such as the union and the intersection; also both of the chaotic incidence matrices and the chaotic adjacency matrices representing the chaotic graphs induced from these operations will be studied. Theorems governing these studies are obtained. Some applications on chaotic graphs are given
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.
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...
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.
A mixed time series model of binomial counts
Khoo, Wooi Chen; Ong, Seng Huat
2015-10-01
Continuous time series modelling has been an active research in the past few decades. However, time series data in terms of correlated counts appear in many situations such as the counts of rainy days and access downloading. Therefore, the study on count data has become popular in time series modelling recently. This article introduces a new mixture model, which is an univariate non-negative stationary time series model with binomial marginal distribution, arising from the combination of the well-known binomial thinning and Pegram's operators. A brief review of important properties will be carried out and the EM algorithm is applied in parameter estimation. A numerical study is presented to show the performance of the model. Finally, a potential real application will be presented to illustrate the advantage of the new mixture model.
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.
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....
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...
The Ohio economy: using time series characteristics in forecasting
James G. Hoehn; James J. Balazsy
1985-01-01
The premise of this study is that the regional economist can better understand the Ohio economy by studying the properties of important Ohio time series that can be identified and quantified through simple regression methods.
Residual diagnostics for cross-section time series regression models
Baum, Christopher F
2001-01-01
These routines support the diagnosis of groupwise heteroskedasticity and cross-sectional correlation in the context of a regression model fit to pooled cross-section time series (xt) data. Copyright 2001 by Stata Corporation.
Review of English textbooks in time series analysis (in Russian)
Stanislav Anatolyev
2008-01-01
This is a survey of most notable time series econometrics texts written in English. The essay reflects the author's opinion, as well as opinions of econometricians expressed in published book reviews.
A Matlab Code for Univariate Time Series Forecasting
Shapour Mohammadi; Hossein Abbasi- Nejad
2005-01-01
This M-File forecasts univariate time series such as stock prices with a feedforward neural networks. It finds best (minimume RMSE) network automatically and uses early stopping method for solving overfitting problem.
Effect of two dead times in series on coincidence measurements
Energy Technology Data Exchange (ETDEWEB)
Funck, E.
1987-01-01
Dead times in series occur in any counting device where detector signals are electronically amplified, selected for pulse height by a discriminator (or pulse-height analyzer) and fed through a dead-time unit producing a dead time, which has very often been designed to establish definite dead time losses. The problem of two dead times in series has been treated by J.W. Muller. No attempt, however, seems to have been made up to now to investigate this problem for the electronics of a coincidence system. In the paper presented here two dead times in series are considered that are found either in one or in both channels of a coincidence system. Correction formulas with experimental evidence are given which allow the deviations from results, which were calculated by taking only one dead time per channel into account, to be estimated.
Neural Networks, Game Theory and Time Series Generation
Metzler, Richard
2002-01-01
This dissertation highlights connections between the fields of neural networks, game theory and time series generation. The concept of antipredictability is explained, and the properties of time series that are antipredictable for several prototypical prediction algorithms (neural networks, Boolean funtions etc.) are studied. The Minority Game provides a framework in which antipredictability arises naturally. Several variations of the MG are introduced and compared, including extensions to mo...
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.
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.
Model-Coupled Autoencoder for Time Series Visualisation
Gianniotis, Nikolaos; Kügler, Sven D.; Tiňo, Peter; Polsterer, Kai L.
2016-01-01
We present an approach for the visualisation of a set of time series that combines an echo state network with an autoencoder. For each time series in the dataset we train an echo state network, using a common and fixed reservoir of hidden neurons, and use the optimised readout weights as the new representation. Dimensionality reduction is then performed via an autoencoder on the readout weight representations. The crux of the work is to equip the autoencoder with a loss function that correctl...
On the prediction of stationary functional time series
Aue, A.; Norinho, DD; Hörmann, S
2012-01-01
© 2015, American Statistical Association. This article addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical tractability and the current lack of advanced functional time series methodology. It is shown here how standard multivariate prediction techniques can be used in this context. The connection between functional and multiva...
Trimmed Granger causality between two groups of time series
Hung, Ying-Chao; Tseng, Neng-Fang; Balakrishnan, Narayanaswamy
2014-01-01
The identification of causal effects between two groups of time series has been an important topic in a wide range of applications such as economics, engineering, medicine, neuroscience, and biology. In this paper, a simplified causal relationship (called trimmed Granger causality) based on the context of Granger causality and vector autoregressive (VAR) model is introduced. The idea is to characterize a subset of “important variables” for both groups of time series so that the underlying cau...
Time series analysis of age related cataract hospitalizations and phacoemulsification
2006-01-01
Background Cataract surgery remains a commonly performed elective surgical procedure in the aging and the elderly. The purpose of this study was to utilize time series methodology to determine the temporal and seasonal variations and the strength of the seasonality in age-related (senile) cataract hospitalizations and phacoemulsification surgeries. Methods A retrospective, cross-sectional time series analysis was used to assess the presence and strength of seasonal and temporal patterns of ag...
Gaussian Processes for Local Polynomial Forecasting of Time Series
Fendick, Kerry
2016-01-01
The samples of a signal obscured by noise constitute an example of a time series frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of historic samples is inadequate for accurately forecasting the signal of each considered in isolation. We develop a new forecasting methodology based on Gaussian process regression that is successful in doing so in examples for which the ...
Time Series Estimates of the Italian Consumer Confidence Indicator
Paradiso, Antonio; Rao, B. Bhaskara; Margani, Patrizia
2011-01-01
This work shows that Italian consumer confidence indicator (CCI) is non-stationary and, therefore, can be estimated with the time series methods. It is found that a long-run relationship exists between CCI, short-term interest rate, industrial production index and the difference between perceived and measured inflation. The use of time series methods to estimate CCI for Italy is a novelty in the literature.
From Local to Global Analysis of Music Time Series
Ligges, Uwe; Weihs, Claus
2004-01-01
Local and more and more global musical structure is analyzed from audio time series by time-series-event analysis with the aim of automatic sheet music production and comparison of singers. Note events are determined and classified based on local spectra, and rules of bar events are identified based on accentuation events related to local energy. In order to compare the performances of different singers global summary measures are defined characterizing the overall performance.
Multiple Time Series Ising Model for Financial Market Simulations
International Nuclear Information System (INIS)
In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated
Geomechanical time series and its singularity spectrum analysis
Czech Academy of Sciences Publication Activity Database
Lyubushin, Alexei A.; Kaláb, Zdeněk; Lednická, Markéta
2012-01-01
Roč. 47, č. 1 (2012), s. 69-77. ISSN 1217-8977 R&D Projects: GA ČR GA105/09/0089 Institutional research plan: CEZ:AV0Z30860518 Keywords : geomechanical time series * singularity spectrum * time series segmentation * laser distance meter Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 0.347, year: 2012 http://www.akademiai.com/content/88v4027758382225/fulltext.pdf
Time Series Classification by Class-Specific Mahalanobis Distance Measures
Prekopcsák, Zoltán; Lemire, Daniel
2010-01-01
To classify time series by nearest neighbors, we need to specify or learn one or several distance measures. We consider variations of the Mahalanobis distance measures which rely on the inverse covariance matrix of the data. Unfortunately --- for time series data --- the covariance matrix has often low rank. To alleviate this problem we can either use a pseudoinverse, covariance shrinking or limit the matrix to its diagonal. We review these alternatives and benchmark them against competitive ...
Automated Feature Design for Time Series Classification by Genetic Programming
Harvey, Dustin Yewell
2014-01-01
Time series classification (TSC) methods discover and exploit patterns in time series and other one-dimensional signals. Although many accurate, robust classifiers exist for multivariate feature sets, general approaches are needed to extend machine learning techniques to make use of signal inputs. Numerous applications of TSC can be found in structural engineering, especially in the areas of structural health monitoring and non-destructive evaluation. Additionally, the fields of process contr...
Adaptive Fourier Analysis For Unequally-Spaced Time Series Data
Liang, Hong
2002-01-01
Adaptive Fourier Analysis For Unequally-Spaced Time Series Data by Hong Liang Robert V. Foutz, Chairman Statistics (ABSTRACT) Fourier analysis, Walsh-Fourier analysis, and wavelet analysis have often been used in time series analysis. Fourier analysis can be used to detect periodic components that have sinusoidal shape; however, it might be misleading when the periodic components are not sinusoidal. Walsh-Fourier analysis is suitable for revealing the rectangular ...
Locally adaptive factor processes for multivariate time series
Durante, Daniele; Scarpa, Bruno; Dunson, David B
2012-01-01
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to mis-calibration of predic...
Time series modelling and forecasting of Sarawak black pepper price
Liew, Venus Khim-Sen; Shitan, Mahendran; Hussain, Huzaimi
2000-01-01
Pepper is an important agriculture commodity especially for the state of Sarawak. It is important to forecast its price, as this could help the policy makers in coming up with production and marketing plan to improve the Sarawak’s economy as well as the farmers’welfare. In this paper, we take up time series modelling and forecasting of the Sarawak black pepper price. Our empirical results show that Autoregressive Moving Average (ARMA) time series models fit the price series well and they have...
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.
Chaotic Rough Particle Swarm Optimization Algorithms
Alatas, Bilal; AKIN, ERHAN
2007-01-01
In this chapter chaotic rough PSO, CRPSO, algorithms that use rough decision variables and rough particles that are based on notion of rough patterns have been proposed. Different chaotic maps have been embedded to adapt the parameters of PSO algorithm. This has been done by using of chaotic number generators each time a random number is needed by the classical PSO algorithm. Twelve PSO methods have been proposed and four chaotic maps have been analyzed in the data mining application. It has ...
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.
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.
Comparison of New and Old Sunspot Number Time Series
Cliver, Edward W.; Clette, Frédéric; Lefévre, Laure; Svalgaard, Leif
2016-05-01
As a result of the Sunspot Number Workshops, five new sunspot series have recently been proposed: a revision of the original Wolf or international sunspot number (Lockwood et al., 2014), a backbone-based group sunspot number (Svalgaard and Schatten, 2016), a revised group number series that employs active day fractions (Usoskin et al., 2016), a provisional group sunspot number series (Cliver and Ling, 2016) that removes flaws in the normalization scheme for the original group sunspot number (Hoyt and Schatten,1998), and a revised Wolf or international number (termed SN) published on the SILSO website as a replacement for the original Wolf number (Clette and Lefèvre, 2016; thttp://www.sidc.be/silso/datafiles). Despite quite different construction methods, the five new series agree reasonably well after about 1900. From 1750 to ~1875, however, the Lockwood et al. and Usoskin et al. time series are lower than the other three series. Analysis of the Hoyt and Schatten normalization factors used to scale secondary observers to their Royal Greenwich Observatory primary observer reveals a significant inhomogeneity spanning the divergence in ~1885 of the group number from the original Wolf number. 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.
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
Chaotic dynamics of propeller singing
Institute of Scientific and Technical Information of China (English)
YU Dapeng; ZHAO Deyou; WANG Yu
2012-01-01
The system of propeller singing is proved for the first time to have the character of chaotic dynamics through the study of the signal time series. The estimation of the topolog- ical dimension, the confirmation of the number of independent variable and the description of the character of attractor trajectory in reconstructed phase space are implemented during the analysis of the system. The result indicates that the system of propeller singing can be recon- structed by the optional delay time tD = 1, the minimal embedding dimension dE = 8, and the reconstructed topological parameter with the fractional correlation dimension D2 = 5.1579 and the positive maximum Lyapunov exponent λtD=0.0771. The results provide a new approach to the further study of the propeller singing phenomenon.
International Nuclear Information System (INIS)
Symbolic transfer entropy (STE) is employed to quantify the dominant direction of information flow between two chaotic-semiconductor-laser time series. The information flow in unidirectionally and bidirectionally coupled systems was analyzed systematically. Numerical results show that the dependence relationship can be revealed if there exists any coupling between two chaotic semiconductor lasers. More importantly, in both unsynchronized and good synchronization regimes, the STE can be used to quantify the direction of information flow between the lasers, although the former case leads to a better identification. The results thus establish STE as an effective tool for quantifying the direction of information flow between chaotic-laser-based systems
Pourdehi, Shabnam; Karimipour, Dena; Karimaghaee, Paknosh
2011-12-01
In this paper, an adaptive output error feedback control scheme is proposed for the lag-synchronization of two time-delayed chaotic systems in the presence of channel time-delay, external disturbances and input nonlinearity. Using the Lyapunov theory, stability of the proposed adaptive controller is proved. Lyapunov-Krasovskii approach is used to deal with the existence of time-delay in the system dynamics. Finally, two numerical simulations are presented to illustrate the effectiveness of the developed method.
Potapov, A.; Ali, M. K.
2001-04-01
We consider the problem of stabilizing unstable equilibria by discrete controls (the controls take discrete values at discrete moments of time). We prove that discrete control typically creates a chaotic attractor in the vicinity of an equilibrium. Artificial neural networks with reinforcement learning are known to be able to learn such a control scheme. We consider examples of such systems, discuss some details of implementing the reinforcement learning to controlling unstable equilibria, and show that the arising dynamics is characterized by positive Lyapunov exponents, and hence is chaotic. This chaos can be observed both in the controlled system and in the activity patterns of the controller.
Detection of flood events in hydrological discharge time series
Seibert, S. P.; Ehret, U.
2012-04-01
The shortcomings of mean-squared-error (MSE) based distance metrics are well known (Beran 1999, Schaeffli & Gupta 2007) and the development of novel distance metrics (Pappenberger & Beven 2004, Ehret & Zehe 2011) and multi-criteria-approaches enjoy increasing popularity (Reusser 2009, Gupta et al. 2009). Nevertheless, the hydrological community still lacks metrics which identify and thus, allow signature based evaluations of hydrological discharge time series. Signature based information/evaluations are required wherever specific time series features, such as flood events, are of special concern. Calculation of event based runoff coefficients or precise knowledge on flood event characteristics (like onset or duration of rising limp or the volume of falling limp, etc.) are possible applications. The same applies for flood forecasting/simulation models. Directly comparing simulated and observed flood event features may reveal thorough insights into model dynamics. Compared to continuous space-and-time-aggregated distance metrics, event based evaluations may provide answers like the distributions of event characteristics or the percentage of the events which were actually reproduced by a hydrological model. It also may help to provide information on the simulation accuracy of small, medium and/or large events in terms of timing and magnitude. However, the number of approaches which expose time series features is small and their usage is limited to very specific questions (Merz & Blöschl 2009, Norbiato et al. 2009). We believe this is due to the following reasons: i) a generally accepted definition of the signature of interest is missing or difficult to obtain (in our case: what makes a flood event a flood event?) and/or ii) it is difficult to translate such a definition into a equation or (graphical) procedure which exposes the feature of interest in the discharge time series. We reviewed approaches which detect event starts and/or ends in hydrological discharge time
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.
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.
Forecasting Compositional Time Series: A State Space Approach
Ralph D Snyder; J. Keith Ord; Anne B. Koehler; Keith R. McLaren; Adrian Beaumont
2015-01-01
A method is proposed for forecasting composite time series such as the market shares for multiple brands. Its novel feature is that it relies on multi-series adaptations of exponential smoothing combined with the log-ratio transformation for the conversion of proportions onto the real line. It is designed to produce forecasts that are both non-negative and sum to one; are invariant to the choice of the base series in the log-ratio transformation; recognized and exploit features such as serial...
Arbitrage, market definition and monitoring a time series approach
Burke, S.; Hunter, J
2012-01-01
This article considers the application to regional price data of time series methods to test stationarity, multivariate cointegration and exogeneity. The discovery of stationary price differentials in a bivariate setting implies that the series are rendered stationary by capturing a common trend and we observe through this mechanism long-run arbitrage. This is indicative of a broader market definition and efficiency. The problem is considered in relation to more than 700 weekly data points on...
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 of...... crossover 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 operator alone. Moreover, we present a specific fitness function which exploits the sparse structure of the break points and which can be evaluated particularly efficiently. The experiments on artificial and real-world time series show that the resulting algorithm detects break points with high...
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...
Rules extraction in short memory time series using genetic algorithms
Fong, L. Y.; Szeto, K. Y.
2001-04-01
Data mining is performed using genetic algorithm on artificially generated time series data with short memory. The extraction of rules from a training set and the subsequent testing of these rules provide a basis for the predictions on the test set. The artificial time series are generated using the inverse whitening transformation, and the correlation function has an exponential form with given time constant indicative of short memory. A vector quantization technique is employed to classify the daily rate of return of this artificial time series into four categories. A simple genetic algorithm based on a fixed format of rules is introduced to do the forecasting. Comparing to the benchmark tests with random walk and random guess, genetic algorithms yield substantially better prediction rates, between 50% to 60%. This is an improvement compared with the 47% for random walk prediction and 25% for random guessing method.
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.
Generalized Dynamic Factor Models for Mixed-Measurement Time Series.
Cui, Kai; Dunson, David B
2014-02-12
In this article, we propose generalized Bayesian dynamic factor models for jointly modeling mixed-measurement time series. The framework allows mixed-scale measurements associated with each time series, with different measurements having different distributions in the exponential family conditionally on time-varying latent factor(s). Efficient Bayesian computational algorithms are developed for posterior inference on both the latent factors and model parameters, based on a Metropolis Hastings algorithm with adaptive proposals. The algorithm relies on a Greedy Density Kernel Approximation (GDKA) and parameter expansion with latent factor normalization. We tested the framework and algorithms in simulated studies and applied them to the analysis of intertwined credit and recovery risk for Moody's rated firms from 1982-2008, illustrating the importance of jointly modeling mixed-measurement time series. The article has supplemental materials available online. PMID:24791133
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.
Multiscale entropy analysis of complex physiologic time series.
Costa, Madalena; Goldberger, Ary L; Peng, C-K
2002-08-01
There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise. PMID:12190613
Wavelet analysis for non-stationary, nonlinear time series
Schulte, Justin A.
2016-08-01
Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.
The Photoplethismographic Signal Processed with Nonlinear Time Series Analysis Tools
International Nuclear Information System (INIS)
Finger photoplethismography (PPG) signals were submitted to nonlinear time series analysis. The applied analytical techniques were: (i) High degree polynomial fitting for baseline estimation; (ii) FFT analysis for estimating power spectra; (iii) fractal dimension estimation via the Higuchi's time-domain method, and (iv) kernel nonparametric estimation for reconstructing noise free-attractors and also for estimating signal's stochastic components
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
AMP: a new time-frequency feature extraction method for intermittent time-series data
Barrack, Duncan; Goulding, James; Hopcraft, Keith; Preston, Simon; Smith, Gavin
2015-01-01
The characterisation of time-series data via their most salient features is extremely important in a range of machine learning task, not least of all with regards to classification and clustering. While there exist many feature extraction techniques suitable for non-intermittent time-series data, these approaches are not always appropriate for intermittent time-series data, where intermittency is characterized by constant values for large periods of time punctuated by sharp and transient incr...
Real Time Clustering of Time Series Using Triangular Potentials
Directory of Open Access Journals (Sweden)
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.
Time Series Outlier Detection Based on Sliding Window Prediction
Directory of Open Access Journals (Sweden)
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.
Entropy measure of stepwise component in GPS time series
Lyubushin, A. A.; Yakovlev, P. V.
2016-01-01
A new method for estimating the stepwise component in the time series is suggested. The method is based on the application of a pseudo-derivative. The advantage of this method lies in the simplicity of its practical implementation compared to the more common methods for identifying the peculiarities in the time series against the noise. The need for automatic detection of the jumps in the noised signal and for introducing a quantitative measure of a stepwise behavior of the signal arises in the problems of the GPS time series analysis. The interest in the jumps in the mean level of the GPS signal is associated with the fact that they may reflect the typical earthquakes or the so-called silent earthquakes. In this paper, we offer the criteria for quantifying the degree of the stepwise behavior of the noised time series. These criteria are based on calculating the entropy for the auxiliary series of averaged stepwise approximations, which are constructed with the use of pseudo-derivatives.
Multi-Scale Dissemination of Time Series Data
DEFF Research Database (Denmark)
Guo, Qingsong; Zhou, Yongluan; Su, Li
2013-01-01
, 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......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......-series compression models. Due to the bandwidth limits regarding to potentially sheer speed of data, it is inevitable to compress and re-compress data along the dissemination paths according to the subscription level of each node. Compression would caused the accuracy loss of data, thus we devise several algorithms...
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 ...
Increment Entropy as a Measure of Complexity for Time Series
Directory of Open Access Journals (Sweden)
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.
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.
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.
Learning of time series through neuron-to-neuron instruction
International Nuclear Information System (INIS)
A model neuron with delayline feedback connections can learn a time series generated by another model neuron. It has been known that some student neurons that have completed such learning under the instruction of a teacher's quasi-periodic sequence mimic the teacher's time series over a long interval, even after instruction has ceased. We found that in addition to such faithful students, there are unfaithful students whose time series eventually diverge exponentially from that of the teacher. In order to understand the circumstances that allow for such a variety of students, the orbit dimension was estimated numerically. The quasi-periodic orbits in question were found to be confined in spaces with dimensions significantly smaller than that of the full phase space
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.
Reconstruction of tritium time series in precipitation of Beijing
International Nuclear Information System (INIS)
Human nuclear activities, especially intensive nuclear tests during the 1960s in the world, caused atmospheric tritium concentration increasing significantly, which provided convenient condition for global water cycle research, especially for tracer dating research of groundwater. However, due to the layout of monitoring sites and other reasons, most parts of the world are lack of monitoring data of tritium concentration in precipitation, which brought difficulties in determining the input function which is essential for groundwater tracer dating technique. Based on the analysis of principles and applicability of present reconstruction methods of tritium time series, the tritium time series in precipitation in Beijing during 1953-2002 was reconstructed using combined methods, including Guanbingjun method, trend surface analysis method, trigonometric interpolation method and correlation method. Furthermore, the best method and the best time series curve were elected through comparison of results of different methods. (authors)
Time series analysis in astronomy: Limits and potentialities
DEFF Research Database (Denmark)
Vio, R.; Kristensen, N.R.; Madsen, Henrik; Wamsteker, W.
2005-01-01
priori physical model there are not many possibilities to obtain interpretable results. For this reason, the practice to develop more and more sophisticated statistical methods of time series analysis is not productive. Only techniques of data analysis developed in a specific physical context can be......In this paper we consider the problem of the limits concerning the physical information that can be extracted from the analysis of one or more time series ( light curves) typical of astrophysical objects. On the basis of theoretical considerations and numerical simulations, we show that with no a...... expected to provide useful results. The field of stochastic dynamics appears to be an interesting framework for such an approach. In particular, it is shown that modelling the experimental time series by means of the stochastic differential equations (SDE) represents a valuable tool of analysis. For...
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.
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.
Fuzzy Time Series: An Application to Tourism Demand Forecasting
Directory of Open Access Journals (Sweden)
Muhammad H. Lee
2012-01-01
Full Text Available Problem statement: Forecasting is very important in many types of organizations since predictions of future events must be incorporated into the decision-making process. In the case of tourism demand, better forecast would help directors and investors make operational, tactical and strategic decisions. Besides that, government bodies need accurate tourism demand forecasts to plan required tourism infrastructures, such as accommodation site planning and transportation development, among other needs. There are many types of forecasting methods. Generally, time series forecasting can be divided into classical method and modern methods. Recent studies show that the newer and more advanced forecasting techniques tend to result in improved forecast accuracy, but no clear evidence shows that any one model can consistently outperform other models in the forecasting competition. Approach: In this study, the performance of forecasting between classical methods (Box-Jenkins methods Seasonal Auto-Regressive Integrated Moving Average (SARIMA, Holt Winters and time series regression and modern methods (fuzzy time series has been compared by using data of tourist arrivals to Bali and Soekarno-Hatta gate in Indonesia as case study. Results: The empirical results show that modern methods give more accurate forecasts compare to classical methods. Chens fuzzy time series method outperforms all the classical methods and others more advance fuzzy time series methods. We also found that the performance of fuzzy time series methods can be improve by using transformed data. Conclusion: It is found that the best method to forecast the tourist arrivals to Bali and Soekarno-Hatta was to be the FTS i.e., method after using data transformation. Although this method known to be the simplest or conventional methods of FTS, yet this result should not be odd since several previous studies also have shown that simple method could outperform more advance or complicated methods.
Multifractal regime detecting method for financial time series
International Nuclear Information System (INIS)
Highlights: • A multifractal regime detecting method (MRDM) introduced based on generalized Hurst exponent. • Multifractal regimes in the KOSPI from 1990 through 2012 are identified. • Surrogated tests are performed for the validation of MRDM. - Abstract: We focus on time varying multifractality in time series and introduce a multifractal regime detecting method (MRDM) adopting a nonparametric statistical test for multifractality based on generalized Hurst exponent (GHE). MRDM is a practical method to discriminate multifractal regimes in a time series of any length using a moving time window approach with the adjustable time window size and the moving interval. MRDM is applied to simulations consisting of both multifractal and monofractal regimes, and the results confirm its validity. Using MRDM, we identify multifractal regimes in the time series of Korea composite stock price index (KOSPI) from 1990 through 2012 and observe the distinct stylized facts of the KOSPI return values in multifractal regimes such as the heavy tail distribution, high kurtosis, and the long memory in volatility. Surrogate tests based on improved amplitude adjusted Fourier transformation (IAAFT) algorithm, normal distribution, and generalized student t distribution are performed for the validation of MDRM, and the probable causes of multifractality in the KOSPI series are discussed
Change detection in a time series of polarimetric SAR images
DEFF Research Database (Denmark)
Skriver, Henning; Nielsen, Allan Aasbjerg; Conradsen, Knut
a certain point 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...... to the complex Wishart distribution and demonstrate its application to change detection in truly multi-temporal, polarimetric SAR data. Results will be shown that demonstrate the difference between applying to time series of polarimetric SAR images, pairwise comparisons or the new omnibus test...
Cross-correlation between time series of vehicles and passengers
Zebende, G. F.; Filho, A. Machado
2009-12-01
We study in this paper a cross-correlation between time series of vehicles and passengers collected in the ferry-boat system (sea route that connects the city of Salvador and Itaparica island, Bahia, Brazil), this study is based on the detrended cross-correlation analysis (DCCA) method. The DCCA method is designed to investigate power-law cross correlations between different simultaneously recorded time series in the presence of nonstationarity. Here in this paper we show that is possible to discriminate cross-correlation between vehicles and passengers and also identify seasonal components.
Time series analysis of banking share returns in Thailand
Directory of Open Access Journals (Sweden)
Sunari Saejiang
2001-06-01
Full Text Available An index is constructed based on an equally weighted portfolio of seven major banking shares in Thailand. A GARCH (1,1 model is fitted to the time series of returns on this index for successive trading day from January 1994 to December 1999. During this period the logarithm of the volatility is well fitted by a stationary time series model comprising an additive combination of a single sinusoidal function with a period of six years, and an ARMA (1,1 model.
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.
Application of nonlinear time series models to driven systems
Energy Technology Data Exchange (ETDEWEB)
Hunter, N.F. Jr.
1990-01-01
In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.
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.
Scaling analysis of multi-variate intermittent time series
Kitt, Robert; Kalda, Jaan
2005-08-01
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similar to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk forecasts: the probability of observing next day a large price movement is (super-universally) inversely proportional to the length of the ongoing low-variability period. Finally, a method is devised for a multi-factor scaling analysis. We apply the simplest, two-factor model to equity index and trading volume time series.
Analytical forms of chaotic spiral arms
Harsoula, M.; Efthymiopoulos, C.; Contopoulos, G.
2016-07-01
We develop an analytical theory of chaotic spiral arms in galaxies. This is based on the Moser theory of invariant manifolds around unstable periodic orbits. We apply this theory to the chaotic spiral arms, which start from the neighbourhood of the Lagrangian points L1 and L2 at the end of the bar in a barred-spiral galaxy. The series representing the invariant manifolds starting at the Lagrangian points L1, L2, or unstable periodic orbits around L1 and L2, yield spiral patterns in the configuration space. These series converge in a domain around every Lagrangian point, called `Moser domain', and represent the orbits that constitute the chaotic spiral arms. In fact, these orbits are not only along the invariant manifolds, but also in a domain surrounding the invariant manifolds. We show further that orbits starting outside the Moser domain but close to it converge to the boundary of the Moser domain, which acts as an attractor. These orbits stay for a long time close to the spiral arms before escaping to infinity.
On the estimation of correlations for irregularly spaced time series
Andersson, Jonas
2007-01-01
In this paper, the problem of calculating covariances and correlations between time series which are observed irregularly and at different points in time, is treated. The problem of dependence between the time stamp process and the return process is especially highlighted and the solution to this problem for a special case is given. Furthermore, estimators based on different interpolation methods are investigated. The covariances are in turn used to estimate a simple regression on such data. ...
Chaotic Vibration Analysis of the Bottom Rotating Drill String
Qilong Xue; Ruihe Wang; Feng Sun; Zhiyuan Huang
2014-01-01
Drill string vibration is a widely studied topic. This paper developed a real-time measurement system near the drilling bit and extracted the lateral vibration, longitudinal vibration time series of bottom rotating drill string. In order to reconstruct the phase space, we estimated the delay time with mutual information and calculated the embedding dimension through Cao’s method. Finally, the chaotic characterization of the system is analyzed by calculating the correlation dimension and the l...
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...
Finite-Time Synchronization of Chaotic Complex Networks with Stochastic Disturbance
Directory of Open Access Journals (Sweden)
Liangliang Li
2014-12-01
Full Text Available This paper is concerned with the problem of finite-time synchronization in complex networks with stochastic noise perturbations. By using a novel finite-time ℒ -operator differential inequality and other inequality techniques, some novel sufficient conditions are obtained to ensure finite-time stochastic synchronization for the complex networks concerned, where the coupling matrix need not be symmetric. The effects of control parameters on synchronization speed and time are also analyzed, and the synchronization time in this paper is shorter than that in the existing literature. The results here are also applicable to both directed and undirected weighted networks without any information of the coupling matrix. Finally, an example with numerical simulations is given to demonstrate the effectiveness of the proposed method.
A Novel Approach for Nonstationary Time Series Analysis with Time-Invariant Correlation Coefficient
Chengrui Liu; Zhihua Wang; Huimin Fu; Yongbo Zhang
2014-01-01
We will concentrate on the modeling and analysis of a class of nonstationary time series, called correlation coefficient stationary series, which commonly exists in practical engineering. First, the concept and scope of correlation coefficient stationary series are discussed to get a better understanding. Second, a theorem is proposed to determine standard deviation function for correlation coefficient stationary series. Third, we propose a moving multiple-point average method to determine th...
Stochastic generation of hourly wind speed time series
International Nuclear Information System (INIS)
In the present study hourly wind speed data of Kuala Terengganu in Peninsular Malaysia are simulated by using transition matrix approach of Markovian process. The wind speed time series is divided into various states based on certain criteria. The next wind speed states are selected based on the previous states. The cumulative probability transition matrix has been formed in which each row ends with 1. Using the uniform random numbers between 0 and 1, a series of future states is generated. These states have been converted to the corresponding wind speed values using another uniform random number generator. The accuracy of the model has been determined by comparing the statistical characteristics such as average, standard deviation, root mean square error, probability density function and autocorrelation function of the generated data to those of the original data. The generated wind speed time series data is capable to preserve the wind speed characteristics of the observed data
Turbulent-Like Behavior of Seismic Time Series
Manshour, P; Sahimi, Muhammad; Peinke, J; Pacheco, Amalio F; Tabar, M Reza Rahimi
2009-01-01
We report on a novel stochastic analysis of seismic time series for the Earth's vertical velocity, by using methods originally developed for complex hierarchical systems, and in particular for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced change of the shapes of the probability density functions (PDF) of the series' increments. Before and close to an earthquake the shape of the PDF and the long-range correlation in the increments both manifest significant changes. For a moderate or large-size earthquake the typical time at which the PDF undergoes the transition from a Gaussian to a non-Gaussian is about 5-10 hours. Thus, the transition represents a new precursor for detecting such earthquakes.
A multiscale statistical model for time series forecasting
Wang, W.; Pollak, I.
2007-02-01
We propose a stochastic grammar model for random-walk-like time series that has features at several temporal scales. We use a tree structure to model these multiscale features. The inside-outside algorithm is used to estimate the model parameters. We develop an algorithm to forecast the sign of the first difference of a time series. We illustrate the algorithm using log-price series of several stocks and compare with linear prediction and a neural network approach. We furthermore illustrate our algorithm using synthetic data and show that it significantly outperforms both the linear predictor and the neural network. The construction of our synthetic data indicates what types of signals our algorithm is well suited for.
Segmentation of time series with long-range fractal correlations
Bernaola-Galván, P.; Oliver, J.L.; Hackenberg, M.; Coronado, A.V.; Ivanov, P.Ch.; Carpena, P.
2012-01-01
Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome. PMID:23645997
Arrows of time and chaotic properties of the cosmic background radiation
International Nuclear Information System (INIS)
We advance a new viewpoint on the connection between the thermodynamical and cosmological arrows of time, which can be traced via the properties of cosmic microwave background (CMB) radiation. We show that in the Friedmann-Robertson-Walker universe with negative curvature there is a necessary ingredient for the existence of the thermodynamical arrow of time. It is based on the dynamical instability of motion along null geodesics in a hyperbolic space. Together with special (de-correlated) initial conditions, this mechanism is sufficient for the thermodynamical arrow, whereas the special initial conditions alone are able to generate only a pre-arrow of time. Since the negatively curved space will expand forever, this provides a direct connection between the thermodynamical and cosmological arrows of time. The structural stability of the geodesic flows on hyperbolic spaces and hence the robustness of the proposed mechanism is especially stressed. We then point out that the main relations of equilibrium statistical thermodynamics (including the second law) do not necessarily depend on any arrow of time. Finally we formulate a curvature anthropic principle, which stipulates the negative curvature as a necessary condition for the time-asymmetric universe with an observer. CMB has to carry the signature of this principle as well. (author)
Practical implementation of nonlinear time series methods The TISEAN package
Hegger, R; Schreiber, T; Hegger, Rainer; Kantz, Holger; Schreiber, Thomas
1998-01-01
Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena despite the fact that very few natural systems have actually been found to be low dimensional deterministic in the sense of the theory. In order to evaluate the long term usefulness of the nonlinear time series approach as inspired by chaos theory, it will be important that the corresponding methods become more widely accessible. This paper, while not a proper review on nonlinear time series analysis, tries to make a contribution to this process by describing the actual implementation of the algorithms, and their proper usage. Most of the methods require the choice of certain parameters for each specific time series application. We will try to give guidance in this respect. The scope and selection of topics in this article, as well as the implementational choices that have ...
The application of the transfer entropy to gappy time series
Energy Technology Data Exchange (ETDEWEB)
Kulp, C.W. [Department of Physics and Astronomy, Lycoming College, Williamsport, PA 17701 (United States)], E-mail: kulp@lycoming.edu; Tracy, E.R. [Department of Physics, The College of William and Mary, Williamsburg, VA 23187-8795 (United States)], E-mail: ertrac@wm.edu
2009-03-23
The application of the transfer entropy to gappy symbolic time series is discussed. Although the transfer entropy can fail to correctly identify the drive-response relationship, it is able to robustly detect phase relationships. Hence, it might still be of use in applications requiring the detection of changes in these relationships.