This paper addresses the notion that many fractional I(d) processes may fall into the ?empty box? category, as discussed in Granger (1999). We present ex ante forecasting evidence based on an updated version of the absolute returns series examined by Ding, Granger and Engle (1993) that 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, with very few models being ?better? than ARFIMA models, based on analysis of point mean square forecast errors (MSFEs), and based on the use of Diebold and Mariano (1995) and Clark and McCracken (2001) predictive accuracy tests. Results are presented for a variety of forecast horizons and for recursive and rolling estimation schemes. The strongest evidence in favor of ARFIMA models arises when various transformations of 5 major stock index returns are examined. For these data, ARFIMA models are frequently found to significantly outperform linear alternatives around one third of the time, and in the case of 1-month ahead predictions of daily returns based on recursively estimated models, this number increases to one half of the time. Overall, it is found that ARFIMA models perform better for greater forecast horizons, while this is clearly not the case for non-ARFIMA models. We provide further support for our findings via examination of the large (215 variable) dataset used in Stock and Watson (2002), and via discussion of a series of Monte Carlo experiments that examine the predictive performance of ARFIMA model.
fractional integration long memory parameter estimation error stock returns long horizon prediction