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Wavelets in Time Series Analysis


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

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

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    Cited by:
    1. Piotr Fryzlewicz & S├ębastien 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.
    2. 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.
    3. 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.
    4. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Working Papers 02-3, Bank of Canada.
    5. 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.
    6. 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.
    7. 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.
    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. 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.


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