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.
Publié le : 2008-08-15
Classification:
Local stationarity,
nonstationary time series,
wavelet spectrum,
autocorrelation wavelet,
change-point,
pointwise adaptive estimation,
quadratic form,
regularization,
62M10,
60G15,
62G10,
62G05
@article{1216237303,
author = {Van Bellegem, S\'ebastien and von Sachs, Rainer},
title = {Locally adaptive estimation of evolutionary wavelet spectra},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1879-1924},
language = {en},
url = {http://dml.mathdoc.fr/item/1216237303}
}
Van Bellegem, Sébastien; von Sachs, Rainer. Locally adaptive estimation of evolutionary wavelet spectra. Ann. Statist., Tome 36 (2008) no. 1, pp. 1879-1924. http://gdmltest.u-ga.fr/item/1216237303/