Multistep Forecasting of Long Memory Series Using Fractional Exponential Models
13 Pages Posted: 31 Oct 2008
Date Written: 2000
Abstract
We develop forecasting methodology for the fractional exponential (FEXP) model. First, we devise algorithms for fastexact computation of the coefficients in the infinite order autoregressive and moving average representations of a FEXPprocess. We also describe an algorithm to accurately approximate the autocovariances and to simulate realizations of theprocess. Next, we present a fast frequency-domain cross validation method for selecting the order of the model. This modelselection method is designed to yield the model which provides the best multistep forecast for the given lead time, withoutassuming that the process actually obeys a FEXP model. Finally, we use the infinite order autoregressive coefficients of afitted FEXP model to construct multistep forecasts of inflation in the United Kingdom. These forecasts are substantiallydifferent than those from a fitted ARFIMA model.
Keywords: Fractional integration, Long-range dependence, Spectral factorization
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