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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
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