Locally adaptive estimation of evolutionary wavelet spectra
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.
Cite
@article{arxiv.0808.1452,
title = {Locally adaptive estimation of evolutionary wavelet spectra},
author = {Sébastien Van Bellegem and Rainer von Sachs},
journal= {arXiv preprint arXiv:0808.1452},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AOS524 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)