Multistep forecasting of long memory series using fractional exponential models

Abstract

We develop forecasting methodology for the fractional exponential (FEXP) model. First, we devise algorithms for fast exact computation of the coefficients in the infinite order autoregressive and moving average representations of a FEXP process. We also describe an algorithm to accurately approximate the autocovariances and to simulate realizations of the process. Next, we present a fast frequency-domain cross validation method for selecting the order of the model. This model selection method is designed to yield the model which provides the best multistep forecast for the given lead time, without assuming that the process actually obeys a FEXP model. Finally, we use the infinite order autoregressive coefficients of a fitted FEXP model to construct multistep forecasts of inflation in the United Kingdom. These forecasts are substantially different than those from a fitted ARFIMA model.