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arXiv · 0808.1452

Locally adaptive estimation of evolutionary wavelet spectra

Sébastien Van Bellegem·Rainer von Sachs
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Abstract

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. 2008-08-11. Locally adaptive estimation of evolutionary wavelet spectra. https://doi.org/10.1214/07-aos524

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