Modified Durbin Method for Accurate Estimation of Moving-Average Models

Abstract

Spectra with narrow valleys can accurately be described with moving-average (MA) models by using only a small number of parameters. Durbin's MA method uses the estimated parameters of a long autoregressive (AR) model to calculate the MA parameters. Probably all the pejorative remarks on the quality of Durbin's method in the literature are based on suboptimal or wrong choices for the method of AR estimation or for the order of the intermediate AR model. Generally, the AR order should considerably be higher than the order of the best predicting AR model, and it should grow with the sample size. Furthermore, the Burg estimates for the AR parameters give the best results because they have the smallest variance of all the AR methods with a small bias. A modified Durbin MA method uses a properly defined number of AR parameters, which was estimated with Burg's method, and outperforms all the other known MA estimation methods, asymptotically as well as in finite samples. The accuracy is generally close to the Cramer-Rao bound.