Estimation of analytic spectral density of Gaussian stationary processes

Research Report SRR98-006

Estimation of analytic spectral density of Gaussian stationary processes

I. Ibragimov

Abstract: In this paper we consider the problem of estimation of the spectral density $f(\lambda )$ of a gaussian stationary sequence (process) on the base of observations $X_t ,0\leq t\leq T$ . We suppose that f belongs to the class of spectral densities analytic and bounded inside a bounded region $G\ni [a,b]$ . We found the rate of the asymptotic minimax risk in $L_p [a,b],1\leq p\leq\infty$ when $T\to\infty$ .

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