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Wavelets in Time Series Analysis

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

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    Bibliographic Info

    Paper provided by Catholique de Louvain - Institut de statistique in its series Papers with number 9901.

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    Length: 16 pages
    Date of creation: 1999
    Date of revision:
    Handle: RePEc:fth:louvis:9901

    Contact details of provider:
    Postal: Universite Catholique de Louvain, Institut de Statistique, Voie du Roman Pays, 34 B-1348 Louvain- La-Neuve, Belgique.

    Related research

    Keywords: TIME SERIES ; STATISTICAL ANALYSIS ; ESTIMATION OF PARAMETERS;

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    Cited by:
    1. Debashis Mondal & Donald Percival, 2010. "Wavelet variance analysis for gappy time series," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(5), pages 943-966, October.
    2. Piotr Fryzlewicz & Hernando Ombao, 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.
    3. 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.
    4. 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.
    5. 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.
    6. Piotr Fryzlewicz & Sébastien Bellegem & Rainer Sachs, 2003. "Forecasting non-stationary time series by wavelet process modelling," Annals of the Institute of Statistical Mathematics, Springer, vol. 55(4), pages 737-764, December.
    7. 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.
    8. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Working Papers 02-3, Bank of Canada.
    9. 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.

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