Adaptive covariance estimation of locally stationary processes. (English) Zbl 0949.62082

Mallat, Stéphane; Papanicolaou, George; Zhang, Zhifeng

Ann. Stat. 26, No. 1, 1-47 (1998).

Let \(X(t)\) be a real-valued zero-mean process with covariance \(R(t,s)= EX(t)X(s)\). The covariance operator is defined for any \(f\in L^2(R)\) by \[ Tf(t)= \int^\infty_{-\infty} R(t,s)f(s)ds. \] It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. The problem of estimation of covariance operators with a “best” basis search is treated. Fast numerical algorithms and their application to examples of locally stationary processes are described.

Reviewer: N.Leonenko (Cardiff)

MSC:

62M15	Inference from stochastic processes and spectral analysis
60G15	Gaussian processes
60G12	General second-order stochastic processes

Keywords:

local cosine bases; adaptive covariance estimation; approximate Karhunen-Loeve basis; time-varying spetrum; locally stationary processes

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