scholarly journals Using Time Deformation to Filter Nonstationary Time Series with Multiple Time-Frequency Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Mengyuan Xu ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Nonstationary Process ◽  
Nonstationary Time Series ◽  
Multiple Time ◽  
Linear Filters ◽  
Time Frequency ◽  
Time Deformation ◽  
Structure Simulation ◽  
Different Types ◽  
Time Varying Frequency

For nonstationary time series consisting of multiple time-varying frequency (TVF) components where the frequency of components overlaps in time, classical linear filters fail to extract components. TheG-filter based on time deformation has been developed to extract components of multicomponentG-stationary processes. In this paper, we explore the wide application of theG-filter for filtering different types of nonstationary processes with multiple time-frequency structure. Simulation examples illustrate that theG-filter can be applied to filter a broad range of multicomponent nonstationary process where TVF components may in fact overlap in time.

scholarly journals G-Filtering Nonstationary Time Series

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Mengyuan Xu ◽  
Krista B. Cohlmia ◽  
Wayne A. Woodward ◽  
Henry L. Gray
Keyword(s):  
Time Series ◽  
Stationary Process ◽  
Nonstationary Time Series ◽  
Linear Filter ◽  
Time Varying ◽  
Linear Filtering ◽  
Original Process ◽  
Filtering Method ◽  
Time Deformation ◽  
Time Varying Frequency

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.

scholarly journals Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

2021 ◽  
Vol 13 (17) ◽  
pp. 3478
Author(s):  
Sorin Nistor ◽  
Norbert-Szabolcs Suba ◽  
Ahmed El-Mowafy ◽  
Michal Apollo ◽  
Zinovy Malkin ◽  
...  
Keyword(s):  
Time Series ◽  
Satellite System ◽  
Phase Lag ◽  
Time Frequency ◽  
Richter Scale ◽  
Different Types ◽  
Before And After ◽  
Position Time Series ◽  
Global Navigation Satellite ◽  
Seasonal Signal

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT).

Understanding changes in environmental time series with time-frequency causality analysis

2020 ◽  
Author(s):  
Maha Shadaydeh ◽  
Yanira Guanche García ◽  
Miguel Mahecha ◽  
Joachim Denzler
Keyword(s):  
Time Series ◽  
Causal Inference ◽  
Causal Effect ◽  
Domain Analysis ◽  
Frequency Component ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Frequency ◽  
Anomalous Event ◽  
Periodic Components

<p>Understanding causal effect relationships between the different variables in dynamical systems is an important and challenging problem in different areas of research such as attribution of climate change, brain neural connectivity analysis, psychology, among many others. These relationships are guided by the process generating them. Hence, detecting changes or new patterns in the causal effect relationships can be used not only for the detection but also for the diagnosis and attribution of changes in the underlying process.</p><p>Time series of environmental time series most often contain multiple periodical components, e.g. daily and seasonal cycles, induced by the meteorological forcing variables. This can significantly mask the underlying endogenous causality structure when using time-domain analysis and therefore results in several spurious links. Filtering these periodic components as preprocessing step might degrade causal inference. This motivates the use of time-frequency processing techniques such as Wavelet or short-time Fourier transform where the causality structure can be examined at each frequency component and on multiple time scales.</p><p>In this study, we use a parametric time-frequency representation of vector autoregressive Granger causality for causal inference. We first show that causal inference using time-frequency domain analysis outperforms time-domain analysis when dealing with time series that contain periodic components, trends, or noise. The proposed approach allows for the estimation of the causal effect interaction between each pair of variables in the system on multiple time scales and hence for excluding links that result from periodic components.</p><p>Second, we investigate whether anomalous events can be identified based on the observed changes in causal relationships. We consider two representative examples in environmental systems: land-atmosphere ecosystem and marine climate. Through these two examples, we show that an anomalous event can indeed be identified as the event where the causal intensities differ according to a distance measure from the average causal intensities. Two different methods are used for testing the statistical significance of the causal-effect intensity at each frequency component.</p><p>Once the anomalous event is detected, the driver of the event can be identified based on the analysis of changes in the obtained causal effect relationships during the time duration of the event and consequently provide an explanation of the detected anomalous event. Current research efforts are directed towards the extension of this work by using nonlinear state-space models, both statistical and deep learning-based ones.</p>

scholarly journals State-space multitaper time-frequency analysis

2017 ◽  
Vol 115 (1) ◽  
pp. E5-E14 ◽  
Author(s):  
Seong-Eun Kim ◽  
Michael K. Behr ◽  
Demba Ba ◽  
Emery N. Brown
Keyword(s):  
Time Series ◽  
State Space ◽  
Statistical Inference ◽  
Gaussian Processes ◽  
Time Series Data ◽  
Nonstationary Time Series ◽  
Series Data ◽  
Parameter Estimates ◽  
Time Varying ◽  
Time Frequency

Time series are an important data class that includes recordings ranging from radio emissions, seismic activity, global positioning data, and stock prices to EEG measurements, vital signs, and voice recordings. Rapid growth in sensor and recording technologies is increasing the production of time series data and the importance of rapid, accurate analyses. Time series data are commonly analyzed using time-varying spectral methods to characterize their nonstationary and often oscillatory structure. Current methods provide local estimates of data features. However, they do not offer a statistical inference framework that applies to the entire time series. The important advances that we report are state-space multitaper (SS-MT) methods, which provide a statistical inference framework for time-varying spectral analysis of nonstationary time series. We model nonstationary time series as a sequence of second-order stationary Gaussian processes defined on nonoverlapping intervals. We use a frequency-domain random-walk model to relate the spectral representations of the Gaussian processes across intervals. The SS-MT algorithm efficiently computes spectral updates using parallel 1D complex Kalman filters. An expectation–maximization algorithm computes static and dynamic model parameter estimates. We test the framework in time-varying spectral analyses of simulated time series and EEG recordings from patients receiving general anesthesia. Relative to standard multitaper (MT), SS-MT gave enhanced spectral resolution and noise reduction (>10 dB) and allowed statistical comparisons of spectral properties among arbitrary time series segments. SS-MT also extracts time-domain estimates of signal components. The SS-MT paradigm is a broadly applicable, empirical Bayes’ framework for statistical inference that can help ensure accurate, reproducible findings from nonstationary time series analyses.

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