MODEL SELECTION AND FORECASTING FOR LONG-RANGE DEPENDENT PROCESSES

Fractionally integrated autoregressive moving-average (ARFIMA) models have proved useful tools in the analysis of time series with long-rang e dependence. However, little is known about various practical issues regarding model selection and estimation methods, and the impact of se lection and estimation methods on forecasts. By means of a large-scale simulation study, we compare three different estimation procedures an d three automatic model-selection criteria on the basis of their impac t on forecast accuracy. Our results endorse the use of both the freque ncy-domain Whittle estimation procedure and the time-domain approximat e MLE procedure of Haslett and Raftery in conjunction with the AIC and SIC selection criteria, but indicate that considerable care should be exercised when using ARFIMA models. In general, we find that simple A RMA models provide competitive forecasts. Only a large number of obser vations and a strongly persistent time series seem to justify the use of ARFIMA models for forecasting purposes.