Shrinkage Estimation of the Memory Parameter in Stationary Gaussian Processes

Abstract

The correct and efficient estimation of memory parameters in a stationary Gaussian processes is an important issue, since otherwise, forecasts based on the resulting time series would be misleading. On the other hand, if the memory parameters are suspected to fall in a smaller subspace through some hypothesis restrictions, it becomes a hard decision whether to use estimators based on the restricted spaces or to use unrestricted estimators over the full parameter space. In this article, we propose James-Stein-type estimators of the memory parameters of a stationary Gaussian times series process, which can efficiently incorporate the hypothetical restrictions. We show theoretically that the proposed estimators are more efficient than the usual unrestricted maximum likelihood estimators over the entire parameter space.