%0 Journal Article
%T Locally adaptive estimation of evolutionary wavelet spectra
%A S¨¦bastien Van Bellegem
%A Rainer von Sachs
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/07-AOS524
%X 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.
%U http://arxiv.org/abs/0808.1452v1