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Wavelets in Time Series Analysis

Author

Listed:
  • Nason, G.P.
  • von Sachs, R.

Abstract

This article reviews the role of wavelets in statistical time series analysis. We survey work that emphasises scale such as estimation of variance and the scale exponent of a process with a specific scale behaviour such as 1/f processes. We present some of our own work on locally stationary wavelet (LSW) processes which model both stationary and some kinds of non-stationary processes. Analysis of time series assuming the LSW model permits identification of an evolutionary wavelet spectrum (EWS) that quantifies the variation in a time series over a particualr state and at a particular time. We address estimation of the EWS and show how our methodology reveals phenomena of interest in an infant electrocardiogram series.

Suggested Citation

  • Nason, G.P. & von Sachs, R., 1999. "Wavelets in Time Series Analysis," Papers 9901, Catholique de Louvain - Institut de statistique.
    • Handle: RePEc:fth:louvis:9901
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    Citations

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    Cited by:

    1. Ben Moews & J. Michael Herrmann & Gbenga Ibikunle, 2018. "Lagged correlation-based deep learning for directional trend change prediction in financial time series," Papers 1811.11287, arXiv.org, revised Nov 2018.
    2. Muhammad Shoaib & Asaad Y. Shamseldin & Sher Khan & Mudasser Muneer Khan & Zahid Mahmood Khan & Tahir Sultan & Bruce W. Melville, 2018. "A Comparative Study of Various Hybrid Wavelet Feedforward Neural Network Models for Runoff Forecasting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(1), pages 83-103, January.
    3. Antonis A. Michis & Guy P. Nason, 2017. "Case study: shipping trend estimation and prediction via multiscale variance stabilisation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2672-2684, November.
    4. Zhao, Xin & Ghaemi Asl, Mahdi & Rashidi, Muhammad Mahdi & Vasa, László & Shahzad, Umer, 2023. "Interoperability of the revolutionary blockchain architectures and Islamic and conventional technology markets: Case of Metaverse, HPB, and Bloknet," The Quarterly Review of Economics and Finance, Elsevier, vol. 92(C), pages 112-131.
    5. Debashis Mondal & Donald Percival, 2010. "Wavelet variance analysis for gappy time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 943-966, October.
    6. Yong-Sik Ham & Kyong-Bok Sonu & Un-Sim Paek & Kum-Chol Om & Sang-Il Jong & Kum-Ryong Jo, 2023. "Comparison of LSTM network, neural network and support vector regression coupled with wavelet decomposition for drought forecasting in the western area of the DPRK," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 116(2), pages 2619-2643, March.
    7. Kawka, Rafael, 2022. "Convergence of spectral density estimators in the locally stationary framework," Econometrics and Statistics, Elsevier, vol. 24(C), pages 94-115.
    8. Stephen Pollock & Iolanda Lo Cascio, 2005. "Orthogonality Conditions for Non-Dyadic Wavelet Analysis," Working Papers 529, Queen Mary University of London, School of Economics and Finance.
    9. Christian M. Hafner, 2012. "Cross-correlating wavelet coefficients with applications to high-frequency financial time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1363-1379, December.
    10. Guy Nason & Kara Stevens, 2015. "Bayesian Wavelet Shrinkage of the Haar-Fisz Transformed Wavelet Periodogram," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-24, September.
    11. Jammazi, Rania & Aloui, Chaker, 2012. "Crude oil price forecasting: Experimental evidence from wavelet decomposition and neural network modeling," Energy Economics, Elsevier, vol. 34(3), pages 828-841.
    12. Ozun, Alper & Cifter, Atilla, 2007. "Modeling Long-Term Memory Effect in Stock Prices: A Comparative Analysis with GPH Test and Daubechies Wavelets," MPRA Paper 2481, University Library of Munich, Germany.
    13. Piotr Fryzlewicz & Sébastien Bellegem & Rainer Sachs, 2003. "Forecasting non-stationary time series by wavelet process modelling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 737-764, December.
    14. Jammazi, Rania & Aloui, Chaker, 2010. "Wavelet decomposition and regime shifts: Assessing the effects of crude oil shocks on stock market returns," Energy Policy, Elsevier, vol. 38(3), pages 1415-1435, March.
    15. Stephen Pollock & Iolanda Lo Cascio, 2005. "Orthogonality Conditions for Non-Dyadic Wavelet Analysis," Working Papers 529, Queen Mary University of London, School of Economics and Finance.
    16. Fryzlewicz, Piotr & Ombao, Hernando, 2009. "Consistent classification of non-stationary time series using stochastic wavelet representations," LSE Research Online Documents on Economics 25162, London School of Economics and Political Science, LSE Library.
    17. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Staff Working Papers 02-3, Bank of Canada.
    18. Vahid Nourani & Mehdi Komasi & Akira Mano, 2009. "A Multivariate ANN-Wavelet Approach for Rainfall–Runoff Modeling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(14), pages 2877-2894, November.
    19. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.
    20. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    21. Tata Subba Rao & Granville Tunnicliffe Wilson & Alessandro Cardinali & Guy P. Nason, 2017. "Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 151-174, March.

    More about this item

    Keywords

    TIME SERIES ; STATISTICAL ANALYSIS ; ESTIMATION OF PARAMETERS;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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