Efficient estimation of multivariate moving average autocovariances

Abstract

SUMMARY This paper proposes a method for estimating the autocovariances of a d -dimensional moving average process of order q . The estimators have the same asymptotic covariance matrix as those obtained by maximizing a Gaussian likelihood, and are obtained by performing a generalized least squares regression of the periodogram on the autocovariances, thus extending Parzen's (1971) estimators for d = 1. An application to least squares prediction is described and the results of a Monte Carlo simulation are presented.