The Annals of Statistics

Locally adaptive estimation of evolutionary wavelet spectra

Sébastien Van Bellegem and Rainer von Sachs

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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.

Article information

Ann. Statist., Volume 36, Number 4 (2008), 1879-1924.

First available in Project Euclid: 16 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G15: Gaussian processes 62G10: Hypothesis testing 62G05: Estimation

Local stationarity nonstationary time series wavelet spectrum autocorrelation wavelet change-point pointwise adaptive estimation quadratic form regularization


Van Bellegem, Sébastien; von Sachs, Rainer. Locally adaptive estimation of evolutionary wavelet spectra. Ann. Statist. 36 (2008), no. 4, 1879--1924. doi:10.1214/07-AOS524.

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