Quasi-Empirical Bayes Methods of Estimation in Arma ( p,q ) Models with Vague Prior Information on MA( q ) 1

Abstract

This paper investigates the asymptotic properties of various estimators of autocorrelations in an ARMA{p,q) model when vague non-sampling information on the moving average part is available. In particular, we discuss the usual MLE {called unrestricted estimator), restricted MLE (based on vague information), preliminary test estimator, shrinkage estimator and the positive rule estimator of the autocorrelations. It is shown that near the prior information on the MA-parameters, the restricted , preliminary test and shrinkage estimators of the autoregressive parameters perform better than the unrestricted estimator, while their superiority changes as MA-parameters divert from the prior informations. The analysis is based on the asymptotic properties of the estimators under contiguous alternatives.