Locally adaptive estimation of evolutionary wavelet spectra

Details Locally adaptive estimation of evolutionary wavelet spectra Locally adaptive estimation of evolutionary wavelet spectra

2008-08-11

arxiv.org/abs/0808.1452v1

Annals of Statistics 2008, Vol. 36, No. 4, 1879-1924

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS524 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS524

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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