Analysis Of Nonstationary Time Series Research Articles

Outlier Detection in Structural Time Series Models: The Indicator Saturation Approach

Abstract Structural change affects the estimation of economic signals, such as the growth rate or the seasonally adjusted series. One important issue that has attracted a great deal of attention in the seasonal adjustment literature is its detection by an expert procedure. The general-to-specific approach to the detection of structural change, which is currently implemented in Autometrics via indicator saturation, has proven to be both practical and effective in the context of stationary dynamic regression models and unit-root autoregressions. By focusing on impulse- and step-indicator saturation, we use Monte Carlo simulations to investigate the performance of this approach for detecting additive outliers and level shifts in the analysis of nonstationary seasonal time series. The reference model is the basic structural model, featuring a local linear trend, possibly integrated of order two, stochastic seasonality and a stationary component. Further, we apply both kinds of indicator saturation to the detection of additive outliers and level shifts in the industrial production series of five European countries.

Network structure of multivariate time series.

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.

Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation

Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.

Search for the 531-day-period wobble signal in the polar motion based on EEMD

Abstract. In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531-day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM series (1962–1977), but cannot be found in the recent PM series (1978–2013) using conventional analysis approaches. By virtue of the demodulation feature of EEMD, the 531 dW can be confirmed to be present in PM based on the differences of the amplitudes and phases between different intrinsic mode functions. Results from three sub-series divided from the EOP C04 series show that the period of the 531 dW is subject to variations, in the range of 530.9–524 days, and its amplitude is also time-dependent (about 2–11 mas). Synthetic tests are carried out to explain why the 531 dW can only be observed in recent 30-year PM time series after using EEMD. The 531 dW is also detected in the two longest available superconducting gravimeter (SG) records, which further confirms the presence of the 531 dW. The confirmation of the 531 dW existence could be significant in establishing a more reasonable Earth rotation model and may effectively contribute to the prediction of the PM and its mechanism interpretation.

Time‐varying ionosonde trend: Case study of Sodankylä hmF2 data 1957–2014

AbstractWe discuss trend analysis of nonstationary ionosonde hmF2 time series measured at Sodankylä Geophysical Observatory (67.4∘N, 26.7∘E), Finland, 1957–2014. We model the hmF2 with a dynamic regression time series model with the following components: a slowly varying background level, seasonal variations, and solar effects. We analyze the time series with a dynamic linear state space model. Such an approach allows model components to vary in time, allowing us to study the dynamic stochastic nature of the underlying long‐term trend. This feature is lacking in most time series models used in atmospheric and environmental long‐term trend analyses. Our objective is to understand the long‐term hmF2 trend with respect to increased levels of carbon dioxide and methane in the atmosphere. Based on model estimates, this phenomenon is predicted to cool the thermosphere and leads to decrease of the altitude of the so‐called F2 layer peak. After accounting for the effects of solar activity variations on the data, we see that the estimated trend shows an almost 30 km decrease of the F2 layer peak during the observation period. The decrease of the peak during 1990–2010 is significantly greater than during earlier observation period.

Time Series in the Study of Seismic Regime of Vrancea (Romania) Seismic Zone

In the series of monthly number of earthquakes is present long-term systematic component. The assumption about stationary of the average value and the variance is rejected. Statistically significant autocorrelation coefficients mean that the time series is not random, and there is some connection between successive levels. In order to predict a series of exponential smoothing method was used. Best model is simple seasonal for the logarithm of the levels, and Winters additive for the square root level of the original series. The research of time series confirms that the ARIMA (0, 1, 2) x (1, 0, 1) s model can be used to the analysis and prediction of uniform non-stationary time series with a nonlinear trend, such as a polynomial of low degree. Prediction for 2012 is computed using simple Simple seasonal, Winters and ARIMA models.

Spectral analysis of surface EMG based on empirical mode decomposition

Muscle fatigue is a common experience in daily life. Some researchers have defined it as the incapacity to maintain the required or expected force. Obviously, force, power and torque recordings as direct measurements of muscle fatigue are difficult to be obtained in one experiment. The main issue when using conventional sEMG variables to quantify fatigue is their poor association with direct measures of fatigue. Therefore, there is a need to develop muscle fatigue approaches that relate changes in sEMG variables with muscle fatigue. The empirical mode decomposition which is a recent tool for the analysis of nonlinear and nonstationary time-series is presented.

Observational evidence for buffeting-induced kink waves in solar magnetic elements

The role of diffuse photospheric magnetic elements in the energy budget of the upper layers of the Sun's atmosphere has been the recent subject of many studies. This was made possible by the availability of high temporal and spatial resolution observations of the solar photosphere, allowing large numbers of magnetic elements to be tracked to study their dynamics. In this work we exploit a long temporal series of seeing-free magnetograms of the solar photosphere to study the effect of the turbulent convection in the excitation of kink oscillations in magnetic elements. We make use of the empirical mode decomposition technique (EMD) in order to study the transverse oscillations of several magnetic flux tubes. This technique permits the analysis of non-stationary time series like those associated to the horizontal velocities of these flux tubes which are continuously advected and dispersed by granular flows. Our primary findings reveal the excitation of low frequency modes of kink oscillations, which are sub-harmonics of a fundamental mode with a $7.6 \pm 0.2$ minute periodicity. These results constitute a strong case for observational proof of the excitation of kink waves by the buffeting of the convection cells in the solar photosphere, and are discussed in light of their possible role in the energy budget of the upper Sun's atmosphere.

Efficient transfer entropy analysis of non-stationary neural time series.

Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these necessary observations, available estimators typically assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble of realizations is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that is suitable for the increased computational demand of the ensemble method's practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method for transfer entropy estimation. We test the performance and robustness of our implementation on data from numerical simulations of stochastic processes. We also demonstrate the applicability of the ensemble method to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscience data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.

Use of Methods of Singular Spectral Analysis and Modeleteka for the Identification of Time Series

Singular spectrum analysis (SSA) is relatively new method for analysis of non-stationary time series. The weakness of SSA is lack of analytical model representation of time series, e.g., as a sum of simple functions, which could be clearer and easier for interpretation than a large number of components in form of time series. In this paper we propose to use variative modeling, based on joint use of SSA and method of modeleteka, for obtaining of analytical model of time series, providing necessary level of adequacy, compactness and interpretability. First, time series are decomposed into components using SSA, significant components are selected using formal indicators (e.g. variance contributed by component, etc.). Second, each significant component is identified according to the purpose of identification with simple and interpretable model from preformed modeleteka. The result is final model of time series in additive or additive-multiplicative form. Applicability of the method is shown on synthetic data and time series of daily changes of water turbidity in the river in the city of Chelyabinsk in 2005.

Nonstationary magnetotelluric data processing with instantaneous parameter

Nonstationarity in electromagnetic data affects the computation of Fourier spectra and therefore the traditional estimation of the magnetotelluric (MT) transfer functions (TF). We provide a TF estimation scheme based on an emerging nonlinear, nonstationary time series analysis tool, called empirical mode decomposition (EMD) and show that this technique can handle nonstationary effects with which traditional methods encounter difficulties. In contrast to previous works that employ EMD for MT data processing, we argue the advantages of a multivariate decomposition, highlight the possibility to use instantaneous parameters, and define the homogenization of frequency discrepancies between data channels. Our scheme uses the robust statistical estimation of transfer functions based on robust principal component analysis and a robust iteratively reweighted least squares regression with a Huber weight function. The scheme can be applied with and without aid of any number of available remote reference stations. Uncertainties are estimated by iterating the complete robust regression, including the robust weight computation, with a bootstrap routine. We apply our scheme to synthetic and real data (Southern Africa) with and without nonstationary character and compare different processing techniques to the one presented here. As a conclusion, nonstationary noise can heavily affect Fourier‐based MT data processing but the presented nonstationary approach is nonetheless able to extract the impedances.

Inference of weighted $V$-statistics for nonstationary time series and its applications

We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle of Fourier analysis. The established theory for $V$-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference of periodograms and spectral densities.

Autocorrelation and cross-correlation in time series of homicide and attempted homicide

We propose in this paper to establish the relationship between homicides and attempted homicides by a non-stationary time-series analysis. This analysis will be carried out by Detrended Fluctuation Analysis (DFA), Detrended Cross-Correlation Analysis (DCCA), and DCCA cross-correlation coefficient, ρDCCA(n). Through this analysis we can identify a positive cross-correlation between homicides and attempted homicides. At the same time, looked at from the point of view of autocorrelation (DFA), this analysis can be more informative depending on time scale. For short scale (days), we cannot identify auto-correlations, on the scale of weeks DFA presents anti-persistent behavior, and for long time scales (n>90 days) DFA presents a persistent behavior. Finally, the application of this new type of statistical analysis proved to be efficient and, in this sense, this paper can contribute to a more accurate descriptive statistics of crime.

A Novel Approach for Nonstationary Time Series Analysis with Time-Invariant Correlation Coefficient

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 the function forms for mean and standard deviation, which can help to improve the analysis precision, especially in the context of limited sample size. Fourth, the conditional likelihood approach is utilized to estimate the model parameters. In addition, we discuss the correlation coefficient stationarity test method, which can contribute to the verification of modeling validity. Monte Carlo simulation study illustrates the authentication of the theorem and the validity of the established method. Empirical study shows that the approach can satisfactorily explain the nonstationary behavior of many practical data sets, including stock returns, maximum power load, China money supply, and foreign currency exchange rate. The effectiveness of these processes is addressed by forecasting performance.

Multi-technique Analysis of the Solar 10.7 cm Radio Flux Time-Series in Relation to Predictability

We studied the predictability of the 10.7 cm solar radio flux by using stationary and non-stationary time-series analysis techniques of fractal theory to find the correlation exponent, the spectral exponent, the Hurst exponent, and the fluctuation exponent of the time series. The Hurst exponent was determined, from which the fractal dimension and consequently the predictability was evaluated. The results suggest that stationary methods of analysis yield inconsistent result, that is, amongst the four techniques used, the values of the exponents show great disparity. While two of the techniques, namely the auto-correlation function analysis and the spectral analysis, indicate long-term positive correlation, the other two methods, specifically the Hurst rescaled range-analysis and the fluctuation analysis, clearly exhibit the anti-correlated nature of the time series. The two non-stationary methods, that is, the discrete wavelet transform and the centered moving-average analysis, yielded values of the Hurst exponent that are indicative of positive correlation, of persistent behavior, and also showed that the time series is predictable to a certain extent.

Coupling analysis of electrocardiogram and electroencephalogram based on improved symbolic transfer entropy

Exploration of the coupling relationship in dynamical system has always been a hot topic of many scholars at home and abroad, the traditional symbolic dynamics analysis method may lead to the results from the serious effect of non-stationary time series. This paper employs coarse graining extraction based on research of original transfer entropy. Through theoretical and experimental analysis, we find that the results of transfer entropy have different distribution trend under different extraction conditions in the coupling analysis of electroencephalogram and electrocardiogram. We choose the best effect of signal data extraction method and apply it to the later application analysis. Furthermore, this paper proposes improvement on the method of time series symbolization, using dynamic adaptive segmentation method. The experimental results show that the whether waking period or sleeping stage, coupling between electroencephalogram and electrocardiogram is more significant when using improved symbolic transfer entropy algorithm. It is also better to capture the dynamic information of the signal and the change of complexity of system dynamics, which is more conductive to clinical testing in practical application and has a better effect on the analysis of non-stationary time series.

Seepage velocities derived from thermal records using wavelet analysis

Summary The main objective of this study was to determine if wavelet analysis can be used as a band-pass filter for non-stationary time series of temperature records. It was demonstrated that this new processing technique is efficient in calculating seepage velocities by using a virtual experiment and field data measured in the Mess Stream, Grand Duchy of Luxembourg, Europe. Temperature time series were measured continuously over a 2-year period in the streambed sediments. The seepage velocity was derived from the one-dimensional analytical solution of Stallman. However, the ubiquitous property of the temperature signal is that it is non-stationary, i.e. the frequency component of the signal becomes a function of time. Instead of applying traditional filtering techniques based on the Fourier transform, we introduce the continuous wavelet transform (CWT) as a band-pass filter to extract the daily component from raw temperature data. For the analysed time series, the estimated seepage velocities based on the amplitude ratio were always negative and within the range of −0.7 to −2.5 m d −1 , indicating gaining conditions prevailing in the Mess Stream. The uncertainty associated with the seepage velocities was calculated by the Monte Carlo analysis allowing several physical parameters of the model to vary over pre-defined intervals with normal distribution. Auxiliary hydraulic measurements in the stream and in the riverbank confirm the dominance of gaining stream conditions. However, the seepage rates based on the thermal records were much higher than the calculated Darcy velocities. This study demonstrates the applicability of continuous wavelet transform as an alternative method to Fourier transform for the analysis of non-stationary temperature time series.

Analysis of persistent nonstationary time series and applications

We give an alternative and unified derivation of the general framework developed in the last few years for analyzing nonstationary time series. A different approach for handling the resulting variational problem numerically is introduced. We further expand the framework by employing adaptive finite element algorithms and ideas from information theory to solve the problem of finding the most adequate model based on a maximum-entropy ansatz, thereby reducing the number of underlying probabilistic assumptions. In addition, we formulate and prove the result establishing the link between the optimal parametrizations of the direct and the inverse problems and compare the introduced algorithm to standard approaches like Gaussian mixture models, hidden Markov models, artificial neural networks and local kernel methods. Furthermore, based on the introduced general framework, we show how to create new data analysis methods for specific practical applications. We demonstrate the application of the framework to data samples from toy models as well as to real-world problems such as biomolecular dynamics, DNA sequence analysis and financial applications.

The Analysis of Nonstationary Time Series Using Regression, Correlation and Cointegration

There are simple well-known conditions for the validity of regression and cor- relation as statistical tools. We analyse by examples the eect of nonstationarity on inference using these methods and compare them to model based inference using the cointegrated vector autoregressive model. Finally we analyse some monthly data from US on interest rates as an illustration of the methods.

Editorial: Special issue on time series analysis in the biological sciences

Editorial: Special issue on time series analysis in the biological sciences