Adaptive covariance estimation of locally stationary processes

Open Access

1 February 1998

journal article
Published by Institute of Mathematical Statistics in The Annals of Statistics

Vol. 26 (1) , 1-47
https://doi.org/10.1214/aos/1030563977

Abstract

It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a "best" local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the best basis.

Keywords

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