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.Statistics Working Papers Serie