CONSISTENT RECURSIVE ESTIMATION OF THE ORDER OF AN AUTOREGRESSIVE MOVING AVERAGE PROCESS

The three-stage Hannan & Rissanen (1982) procedure for selecting the order of an autoregressive moving average, ARMA, process is considered. An argument analogous to that used by Akaike (1970) when deriving his Final Prediction Error (FPE) criterion is adopted to derive a criterion to be used at Stage II. The asymptotic distribution of the estimated ARMA coefficients is derived, and an expression for the one-step mean squared error of prediction with estimated coefficients is given. The bias in estimating the parameters is examined. The proposed criterion is shown to be consistent. The finite sample behaviour relative to the corrected BIC criterion of Hannan & Kavalieris (1984) is investigated by a simulation study, and a comparison with a likelihood-based procedure of order selection is carried out.