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-range dependence. However, little is known about various practical issues regarding model selection and estimation methods, and the impact of selection and estimation methods on forecasts. By means of a large-scale simulation study, the paper compares three different estimation procedures and three automatic model-selection criteria on the basis of their impact on forecast accuracy. The results endorse the use of both the frequency-domain Whittle estimation procedure and the time-domain approximate MLE procedure of Haslett and Raftery in conjunction with the AIC and SIC selection criteria, but indicate that considerable case should be exercised when using ARFIMA models. In general, it is found that simple ARMA models provide competitive forecasts. Only a large number of observations and a strongly persistent time series seem to justify the use of ARFIAM models for forecasting purposes.