Optimal instrumental variable estimates of the AR parameters of an ARMA process

The modified Yule-Walker (MYW) equations for estimating the AR parameters of an ARMA process are presented as a special case of an instrumental variable (IV) method. The consistency and accuracy of the AR parameter estimates are studied. It is shown that estimation accuracy increases monotonically with the number of MYW equations for an optimal choice of the weighting matrix used in the least-squares solution of these equations. The asymptotic error covariance of the optimal IV method is shown to equal that of the prediction error method.