The best order of long autoregressive models for moving average estimation

Durbin´s method for Moving Average (MA) estimation uses the estimated parameters of a long AutoRegressive (AR) model to compute the desired MA parameters. A theoretical order for that long AR model is ∞, but very high AR orders lead to inaccurate MA models in the finite sample practice. A new theoretical argument is presented to derive an expression for the best finite long AR order for a known MA process and a given sample size. Intermediate AR models of precisely that order produce the most accurate MA models. This new order differs from the best AR order to be used for prediction. An algorithm is presented that enables use of the theory for the best long AR order in known processes to data of an unknown process.