Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes

Yoshihide Kakizawa

Journal of Time Series Analysis, 1999, vol. 20, issue 5, 551-558

Abstract: In this note certain results obtained by Porat (J. Time Ser. Anal. 8 (1987), 205–20) and Kakizawa and Taniguchi (J. Time Ser. Anal. 15 (1994), 303–11) concerning the asymptotic efficiency of sample autocovariances of a zero‐mean Gaussian stationary process are extended to the case of m‐vector processes. It is shown that, for Gaussian vector AR(p) processes, the sample autocovariance matrix at lag k is asymptotically efficient if 0 ≤k≤p. Further, none of the sample autocovariance matrices is asymptotically efficient for Gaussian vector MA(q) processes.

Date: 1999
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