scholarly journals Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

2019 ◽  
Vol 9 (7) ◽  
pp. 1345 ◽  
Author(s):  
Manel Rhif ◽  
Ali Ben Abbes ◽  
Imed Farah ◽  
Beatriz Martínez ◽  
Yanfang Sang
Keyword(s):  
Applied Sciences ◽  
Time Series ◽  
Wavelet Transform ◽  
Learning Algorithm ◽  
Decomposition Methods ◽  
Stationary Time Series ◽  
Time Frequency ◽  
Stationary Time ◽  
Wavelet Selection ◽  
Selection Of

Non-stationary time series (TS) analysis has gained an explosive interest over the recent decades in different applied sciences. In fact, several decomposition methods were developed in order to extract various components (e.g., seasonal, trend and abrupt components) from the non-stationary TS, which allows for an improved interpretation of the temporal variability. The wavelet transform (WT) has been successfully applied over an extraordinary range of fields in order to decompose the non-stationary TS into time-frequency domain. For this reason, the WT method is briefly introduced and reviewed in this paper. In addition, this latter includes different research and applications of the WT to non-stationary TS in seven different applied sciences fields, namely the geo-sciences and geophysics, remote sensing in vegetation analysis, engineering, hydrology, finance, medicine, and other fields, such as ecology, renewable energy, chemistry and history. Finally, five challenges and future works, such as the selection of the type of wavelet, selection of the adequate mother wavelet, selection of the scale, the combination between wavelet transform and machine learning algorithm and the interpretation of the obtained components, are also discussed.

On a criterion for the selection of models for stationary time series

Metrika ◽  
1985 ◽  
Vol 32 (1) ◽  
pp. 181-196
Author(s):  
H. Linhart ◽  
P. Volkers
Keyword(s):  
Time Series ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Selection Of

scholarly journals The Fourier decomposition method for nonlinear and non-stationary time series analysis

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160871 ◽  
Author(s):  
Pushpendra Singh ◽  
Shiv Dutt Joshi ◽  
Rakesh Kumar Patney ◽  
Kaushik Saha
Keyword(s):  
Time Series ◽  
Decomposition Method ◽  
Fourier Method ◽  
Stationary Time Series ◽  
Decomposition Algorithms ◽  
Intrinsic Structure ◽  
Fourier Decomposition ◽  
Time Frequency ◽  
Stationary Time ◽  
Adaptive Fourier Decomposition

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

scholarly journals A Survey on Change Detection and Time Series Analysis with Applications

2021 ◽  
Vol 11 (13) ◽  
pp. 6141
Author(s):  
Ebrahim Ghaderpour ◽  
Spiros D. Pagiatakis ◽  
Quazi K. Hassan
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Change Detection ◽  
Computer Time ◽  
Decomposition Methods ◽  
Stationary Time Series ◽  
Detection Methods ◽  
Spectral Leakage ◽  
Time Frequency ◽  
Series Analysis

With the advent of the digital computer, time series analysis has gained wide attention and is being applied to many fields of science. This paper reviews many traditional and recent techniques for time series analysis and change detection, including spectral and wavelet analyses with their advantages and weaknesses. First, Fourier and least-squares-based spectral analysis methods and spectral leakage attenuation methods are reviewed. Second, several time-frequency decomposition methods are described in detail. Third, several change or breakpoints detection methods are briefly reviewed. Finally, some of the applications of the methods in various fields, such as geodesy, geophysics, remote sensing, astronomy, hydrology, finance, and medicine, are listed in a table. The main focus of this paper is reviewing the most recent methods for analyzing non-stationary time series that may not be sampled at equally spaced time intervals without the need for any interpolation prior to the analysis. Understanding the methods presented herein is worthwhile to further develop and apply them for unraveling our universe.

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