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