A direct representation for the large-sample maximum likelihood estimator of a Gaussian autoregressive-moving: average process

Abstract

SUMMARY A simple procedure is described for obtaining the estimator of the parameters of an autoregressive-moving average process. The estimator is derived from the maximum likelihood procedure assuming Gaussian residuals by making two simplifying assumptions which are negligible in large samples. Components of the estimator are expressed as linear combinations of a suitable set of sample serial correlations or as a rational function of such linear combinations.