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.