Improved estimation for the autocovariances of a Gaussian stationary process

For a Gaussian stationary process with mean mu and autocovariance function. gamma(.), we consider to improve the usual sample autocovariances with respect to the mean squares error (MSE) loss. For the cases mu = 0 and mu not equal 0, we propose sort of empirical Bayes type estimators (Gamma) over cap and (Gamma) over cap, respectively. Then their MSE improvements upon the usual sample autocovariances are evaluated in terms of the spectral density of the process. Concrete examples for them are provided. We observe that if the process is near to a unit root process the improvement becomes quite large. Thus, consideration for estimators of this type seems important in many fields, e.g., econometrics.