Autoregressive model orders for Durbin's MA and ARMA estimators

Durbin’s methods for moving average (MA) and autoregressive-moving average (ARMA) estimation use the parameters of a long AR model to compute the MA parameters. Linear regression theory is applied to find the best AR order. This yields two different orders: one for the best predicting AR model and another one for the long AR model with the best parameter accuracy, as intermediate for Durbin’s estimates. Both orders increase with the sample size and have no finite limiting value.