A method for autoregressive-moving average estimation

Abstract

The problem considered is that of estimating an autoregressive-moving average system, including estimating the degrees of the autoregressive and moving average lag operators. The basic method is that introduced by Hannan & Rissanen (1982). However, that method may sometimes overestimate the degrees and modifications are here introduced to correct this. The problem is itself due to the use of a long autoregression, of order c log T when T is large, in the first stage of the process. The effect of this is investigated and in particular its effect on the speed of convergence of the estimates.