An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series

This paper addresses the notion that many fractional I ( d ) processes may fall into the “empty box” category, as discussed in Granger (Aspects of research strategies for time series analysis, Presentation to the Conference on New Developments in Time Series Economics, Yale University, 1999). We present ex ante forecasting evidence which suggests that ARFIMA models estimated using a variety of standard estimation procedures yield “approximations” to the true unknown underlying DGPs that sometimes provide significantly better out-of-sample predictions than AR, MA, ARMA, GARCH, and related models, based on analysis of point mean-square forecast errors (MSFEs), and based on the use of predictive accuracy tests. The strongest evidence in favor of ARFIMA models arises when various transformations of 5 major stock index returns are examined. Additional evidence based on analysis of the Stock and Watson (J. Bus. Econom. Stat. 20 (2002) 147–162) data set, the returns series data set examined by Ding et al. (J. Empirical Finance 1 (1993) 83–106), and based on a series of Monte Carlo experiments is also discussed.