Estimation of the Moving‐average Representation of a Stationary Process by Autoregressive Model Fitting

Abstract.The Hannan‐Rissanen procedure for recursive order determination of an autoregressive moving‐average process provides ‘non‐parametric’ estimators of the coefficientsb(u), say, of the moving‐average representation of a stationary process by auto‐regressive model fitting, and also that of the cross‐covariances,c(u), between the process and its linear innovations. An alternative ‘autoregressive’ estimator of theb(u) is obtained by inverting the autoregressive transfer function. Some uses of these estimators are discussed, and their asymptotic distributions are derived by requiring that the orderkof the fitted autoregression approaches infinity simultaneously with the lengthTof the observed time series. The question of bias in estimating the parameters is also examined.