Out-of-sample forecast errors in misspecific perturbed long memory processes

In this paper we examine the relative increase in mean square forecast error fro fitting a weakly stationary process to the series of interest when in fact the true model is a so-called perturbed long-memory process recently introduced by Granger and Marmol (1997). This model has the property of being unidentifiable from a white noise process on the basis of the correlogram and the usual rule-of-thumbs in the Box-Jenkins methodology. We prove that this kind of missspecification can lead to serious errors in terms of forecasting. We also show that corrections based on the AR(1) model can in some cases partially solve the problem. Received: March 15, 1999; revised version: February 14, 2000