We discuss the problem of shrinkage estimation for the autocovariance matrix of a Gaussian stationary vector-valued process to improve on the usual sample autocovariance matrix with respect to the mean squares error. We propose a kind of empirical Bayes estimators when the mean of the stochastic process is zero and non-zero. We show that the shrinkage estimators dominate the usual estimators, and the asymptotic risk differences are similar to that of scalar-valued Gaussian stationary processes.

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... This result seems to be useful for the autocovariance estimation with vectorvalued dependent observations.