Model selection and forecasting for long-range dependent processes

Nuno Crato · Bonnie K. Ray

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Forecasting Techniques and Applications Complex Systems and Time Series Analysis Time Series Analysis and Forecasting

Abstract

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, we compare three different estimation procedures and three automatic model-selection criteria on the basis of their impact on forecast accuracy. Our 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 care should be exercised when using ARFIMA models. In general, we find 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 ARFIMA models for forecasting purposes.

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References

1968Fractional Brownian Motions, Fractional Noises and Applications 1980AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING 1983THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS 1981Fractional Differencing 1992Maximum likelihood estimation of stationary univariate fractionally integrated time series models 1989Space-Time Modelling with Long-Memory Dependence: Assessing Ireland's Wind Power Resource 1989Long memory and persistence in aggregate output 1993A Fractional Cointegration Analysis of Purchasing Power Parity

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