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

The correlogram is not a useful diagnosis tool in the presence of long-memory or long range depedent time series. The aim of this paper is to illustrate this claim by examining the relative increase in mean square forecast error from fitting a weakly stationary process to the series of interest hen 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 misspecification can lead to serious errors in terms of forecasting.