The approximation of long-memory processes by an ARMA model

A mean square error criterion is proposed in this paper to provide a system atic approach to approximate a long-memory time series by a short-memory AR MA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional mov ing average long-memory time series. Performances of the ARMA(1,1) approxim ation as compared to using an ARFIMA model are illustrated by both computat ions and an application to the Nile river series. Results derived in this p aper shed light on the forecasting issue of a long-memory process. Copyrigh t (C) 2001 John Wiley & Sons, Ltd.