Wavelets in Time Series Analysis
AbstractThis 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 InfoPaper provided by Catholique de Louvain - Institut de statistique in its series Papers with number 9901.
Length: 16 pages
Date of creation: 1999
Date of revision:
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Postal: Universite Catholique de Louvain, Institut de Statistique, Voie du Roman Pays, 34 B-1348 Louvain- La-Neuve, Belgique.
TIME SERIES ; STATISTICAL ANALYSIS ; ESTIMATION OF PARAMETERS;
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- 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.
- Ozun, Alper & Cifter, Atilla, 2007.
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- 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.
- 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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