# zbMATH — the first resource for mathematics

An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series. (English) Zbl 1337.62344
Summary: This paper addresses the notion that many fractional I($$d$$)I($$d$$) processes may fall into the “empty box” category, as discussed in Granger. 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 J. H. Stock and M. W. Watson [“Macroeconomic forecasting using diffusion indexes”, J. Bus. Econom. Stat. 20, No. 2, 147–162 (2002; doi:10.1198/073500102317351921)] data set, the returns series data set examined by Z. Ding, C. W. J. Granger and R. F. Engle [“A long memory property of stock market returns and a new model”, J. Emp. Financ. 1, No. 1, 83–106 (1993; doi:10.1016/0927-5398(93)90006-D)], and based on a series of Monte Carlo experiments is also discussed.

##### MSC:
 62P20 Applications of statistics to economics 91B84 Economic time series analysis
Full Text: