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August 2008 Locally adaptive estimation of evolutionary wavelet spectra
Sébastien Van Bellegem, Rainer von Sachs
Ann. Statist. 36(4): 1879-1924 (August 2008). DOI: 10.1214/07-AOS524


We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on scales. We propose a pointwise adaptive estimator of the time-varying spectrum. The behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum.


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Sébastien Van Bellegem. Rainer von Sachs. "Locally adaptive estimation of evolutionary wavelet spectra." Ann. Statist. 36 (4) 1879 - 1924, August 2008.


Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1142.62067
MathSciNet: MR2435459
Digital Object Identifier: 10.1214/07-AOS524

Primary: 62M10
Secondary: 60G15 , 62G05 , 62G10

Keywords: autocorrelation wavelet , Change-point , local stationarity , nonstationary time series , pointwise adaptive estimation , quadratic form , regularization , wavelet spectrum

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 4 • August 2008
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