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

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.

[1]  Mohammed Azmi Al-Betar,et al.  Hybridizing β-hill climbing with wavelet transform for denoising ECG signals , 2018, Inf. Sci..

[2]  V. Chowdary,et al.  Wavelet and non-parametric statistical based approach for long term land cover trend analysis using time series EVI data , 2018, Geocarto International.

[3]  Russel Pears,et al.  A wavelet approach for precursor pattern detection in time series , 2018, Journal of Electrical Systems and Information Technology.

[4]  Hurtado Abril,et al.  Generación de un índice espectro-temporal para la identificación de zonas afectadas por deforestación usando imágenes Landsat. , 2020 .

[5]  François Benhmad.  Modeling nonlinear Granger causality between the oil price and U.S. dollar: A wavelet based approach , 2012 .

[6]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[7]  Yan-Fang Sang,et al.  Discussion on the Choice of Decomposition Level for Wavelet Based Hydrological Time Series Modeling , 2016 .

[8]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[9]  Jérôme Gilles,et al.  Empirical Wavelet Transform , 2013, IEEE Transactions on Signal Processing.

[10]  Annette Witt,et al.  Holocene climate variability on millennial scales recorded in Greenland ice cores , 2005 .

[11]  Marco Gallegati,et al.  Wavelet analysis of stock returns and aggregate economic activity , 2008, Comput. Stat. Data Anal..

[12]  David Labat,et al.  Recent advances in wavelet analyses: Part 1. A review of concepts , 2005 .

[13]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[14]  Mikko Ranta,et al.  Contagion among major world markets: a wavelet approach , 2013 .

[15]  Ruqiang Yan,et al.  Base wavelet selection criteria for non-stationary vibration analysis in bearing health diagnosis , 2007 .

[16]  Haizhong An,et al.  Evolution of world crude oil market integration and diversification: A wavelet-based complex network perspective , 2017 .

[17]  Dong Wang,et al.  Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales , 2011, Entropy.

[18]  A. Mathur,et al.  Denoising and wavelet-based feature extraction of MODIS multi-temporal vegetation signatures , 2005, International Workshop on the Analysis of Multi-Temporal Remote Sensing Images, 2005..

[19]  Ernesto C. Pereira,et al.  Corrosion of AISI 1020 steel in crude oil studied by the electrochemical noise measurements , 2015 .

[20]  朴英超.  Change Detection Of MODIS Time Series Using A Wavelet Transform , 2012 .

[21]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[22]  Wei Wei,et al.  The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns , 2005, Plant Ecology.

[23]  Hahn-Shik Lee.  International transmission of stock market movements: a wavelet analysis , 2004 .

[24]  Surjya K. Pal,et al.  Tool wear monitoring and selection of optimum cutting conditions with progressive tool wear effect and input uncertainties , 2011, J. Intell. Manuf..

[25]  Atle Mysterud,et al.  Linking climate change to lemming cycles , 2008, Nature.

[26]  Wieslaw J. Staszewski,et al.  Wavelet-based Frequency Response Function for time-variant systems—An exploratory study , 2014 .

[27]  Yuan Lu,et al.  A hybrid wavelet de‐noising and Rank‐Set Pair Analysis approach for forecasting hydro‐meteorological time series , 2018, Environmental research.

[28]  Donald B. Percival,et al.  An introduction to wavelet analysis with applications to vegetation time series , 2004 .

[29]  Michael Unser,et al.  A review of wavelets in biomedical applications , 1996, Proc. IEEE.

[30]  O. Kisi,et al.  Wavelet-based variability on streamflow at 40-year timescale in the Black Sea region of Turkey , 2018, Arabian Journal of Geosciences.

[31]  D. Gabor,et al.  Theory of communication. Part 1: The analysis of information , 1946 .

[32]  Hla Myo Tun,et al.  Analysis on ECG Data Compression Using Wavelet Transform Technique , 2017 .

[33]  Ka-Ming Lau,et al.  Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing , 1995 .

[34]  J. Polanco-Martínez,et al.  Estimation of the significance of the Foster’s wavelet spectrum by means of a permutation test and its application for paleoclimate record , 2018, BOLETÍN GEOLÓGICO Y MINERO.

[35]  Bernard Cazelles,et al.  French economic cycles: a wavelet analysis of French retrospective GNP series , 2009 .

[36]  F. J. García-Haro,et al.  Characterizing land condition variability in Ferlo, Senegal (2001–2009) using multi-temporal 1-km Apparent Green Cover (AGC) SPOT Vegetation data , 2011 .

[37]  Wavelet-Based Test for Time Series Non-Stationarity 1 , .

[38]  J. Polanco-Martínez,et al.  A pre-crisis vs. crisis analysis of peripheral EU stock markets by means of wavelet transform and a nonlinear causality test , 2018 .

[39]  J. Sáenz,et al.  Wavelet analysis of correlation among Canary Islands octopus captures per unit effort, sea-surface temperatures and the North Atlantic Oscillation , 2011 .

[40]  J. Fernández-Macho.  Time-localized wavelet multiple regression and correlation , 2018 .

[41]  Srinivasa Rao Rayapudi,et al.  DWT based bearing fault detection in induction motor using noise cancellation , 2016 .

[42]  Yves Meyer,et al.  Wavelets, Vibrations and Scalings , 1997 .

[43]  J. Fernández-Macho,et al.  A multi-resolution and multivariate analysis of the dynamic relationships between crude oil and petroleum-product prices , 2018, Applied Energy.

[44]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[45]  Xiaoliang Lu,et al.  Removal of Noise by Wavelet Method to Generate High Quality Temporal Data of Terrestrial MODIS Products , 2007 .

[46]  P. Webster,et al.  Interdecadal changes in the ENSO-monsoon system , 1999 .

[47]  Praveen Kumar,et al.  Wavelet Analysis in Geophysics: An Introduction , 1994 .

[48]  B. Martínez,et al.  Comparative study of three satellite image time-series decomposition methods for vegetation change detection , 2018 .

[49]  J. Kingsbury.  The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance , 2004 .

[50]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[51]  Maria Joana Soares,et al.  Using wavelets to decompose the time–frequency effects of monetary policy , 2008 .

[52]  Paul S Addison,et al.  Wavelet transforms and the ECG: a review , 2005, Physiological measurement.

[53]  James B. Ramsey,et al.  The contribution of wavelets to the analysis of economic and financial data , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[54]  Marco Gallegati,et al.  A wavelet-based approach to test for financial market contagion , 2012, Comput. Stat. Data Anal..

[55]  Vadim A. Krysko,et al.  Wavelet modeling and prediction of the stability of states: the Roman Empire and the European Union , 2015, Commun. Nonlinear Sci. Numer. Simul..

[56]  K. Potočki,et al.  AN OVERVIEW OF THE APPLICATIONS OF WAVELET TRANSFORM FOR DISCHARGE AND SUSPENDED SEDIMENT ANALYSIS , 2017 .

[57]  Michael Weniger,et al.  Spatial verification using wavelet transforms: a review , 2016, 1605.03395.

[58]  Ajay Kalra,et al.  Multi-Scale Correlation between the Western U.S. Snow Water Equivalent and ENSO/PDO Using Wavelet Analyses , 2017, Water Resources Management.

[59]  M. Gilabert,et al.  Vegetation dynamics from NDVI time series analysis using the wavelet transform , 2009 .

[60]  António Rua,et al.  International comovement of stock market returns: a wavelet analysis , 2009 .

[61]  Maria Joana Soares,et al.  Oil and the macroeconomy: using wavelets to analyze old issues , 2011 .

[62]  Joseph P. Coughlan,et al.  The Lead–Lag Relationship between Oil Futures and Spot Prices—A Literature Review , 2018, International Journal of Financial Studies.

[63]  Rita Traversi,et al.  Generalization of the cross-wavelet function , 2017 .

[64]  A. Gunasekaran,et al.  Investment horizon heterogeneity and wavelet: Overview and further research directions , 2015 .

[65]  C. Pinho,et al.  Time Frequency Effects on Market Indices: World Commovements , 2009 .

[66]  Ram Bilas Pachori,et al.  Fourier-Bessel series expansion based empirical wavelet transform for analysis of non-stationary signals , 2018, Digit. Signal Process..

[67]  D. Wijaya,et al.  Information Quality Ratio as a novel metric for mother wavelet selection , 2017 .

[68]  Amel Abdoullah Ahmed Dghais,et al.  A study of stationarity in time series by using wavelet transform , 2014 .

[69]  Javier Fernández-Macho,et al.  Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets , 2012 .

[70]  Luís Aguiar-Conraria,et al.  The Continuous Wavelet Transform: Moving Beyond Uni‐ and Bivariate Analysis , 2014 .

[71]  T. Sakamoto,et al.  A crop phenology detection method using time-series MODIS data , 2005 .

[72]  X. Liang,et al.  Rectification of the Bias in the Wavelet Power Spectrum , 2007 .

[73]  Peter Guttorp,et al.  Wavelet analysis of covariance with application to atmospheric time series , 2000 .

[74]  Aslak Grinsted,et al.  Nonlinear Processes in Geophysics Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series , 2022 .

[75]  Todd R. Ogden,et al.  Wavelet Methods for Time Series Analysis , 2002 .

[76]  Yong Liu,et al.  Wavelet-Based Hydrological Time Series Forecasting , 2016 .

[77]  W. Soon,et al.  A review of Holocene solar-linked climatic variation on centennial to millennial timescales: Physical processes, interpretative frameworks and a new multiple cross-wavelet transform algorithm , 2014 .

[78]  Pradip Sircar,et al.  A novel approach for automated detection of focal EEG signals using empirical wavelet transform , 2016, Neural Computing and Applications.

[79]  J. Vik,et al.  Wavelet analysis of ecological time series , 2008, Oecologia.

[80]  E. Foufoula‐Georgiou,et al.  Wavelet analysis for geophysical applications , 1997 .

[81]  C. D. Bella,et al.  Multi-Temporal Analysis of Remotely Sensed Information Using Wavelets , 2012 .

[82]  Yan-Fang Sang,et al.  A review on the applications of wavelet transform in hydrology time series analysis , 2013 .

[83]  Jasmin Kevric,et al.  Performance evaluation of empirical mode decomposition, discrete wavelet transform, and wavelet packed decomposition for automated epileptic seizure detection and prediction , 2018, Biomed. Signal Process. Control..

[84]  P. C. Russell,et al.  Extraction of information from acoustic vibration signals using Gabor transform type devices , 1998 .

[85]  R. Gencay,et al.  An Introduction to Wavelets and Other Filtering Methods in Finance and Economics , 2001 .

[86]  Philippe Masset.  Analysis of financial time series using wavelet methods , 2015 .

[87]  J. Adamowski,et al.  Investigation of the scaling characteristics of LANDSAT temperature and vegetation data: a wavelet-based approach , 2017, International Journal of Biometeorology.

[88]  D. Khare,et al.  Trend analysis using discrete wavelet transform (DWT) for long-term precipitation (1851–2006) over India , 2017 .

[89]  Truong Q. Nguyen,et al.  Forecasting of Solar Photovoltaic System Power Generation Using Wavelet Decomposition and Bias-Compensated Random Forest , 2017, 2017 Ninth Annual IEEE Green Technologies Conference (GreenTech).

[90]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[91]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[92]  Dong Wang,et al.  The relation between periods’ identification and noises in hydrologic series data , 2009 .

[93]  Aviral Kumar Tiwari,et al.  Continuous wavelet transform and rolling correlation of European stock markets , 2016 .

[94]  Fulei Chu,et al.  Application of the wavelet transform in machine condition monitoring and fault diagnostics: a review with bibliography , 2004 .