Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum

This article defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cramér (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time-localized autocovariance. We illustrate our theory with a pedagogical example based on discrete non- decimated Haar wavelets and also a real medical time series example.

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Document type	Document de travail (Working Paper)
Publication date	1998
Language	Anglais
Number of pages	25 pages
Collection	STAT Discussion Paper - 9822
Affiliation	UCL - EUEN/STAT - Institut de statistique
Links	http://hdl.handle.net/2078.1/91343[Handle] http://sites.uclouvain.be/IAP-Stat-Phase-V-VI/ISBApub/ISBAdp.html#1998

See also
	[boreal:90554]	Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum