Semiparametric and Nonparametric Testing for Long Memory: A Monte Carlo Study

The nite sample properties of three semiparametric estimators, several versions of the modiied rescaled range, MRR, and three versions of the GHURST estimator are investigated. Their power and size for testing for long memory under short-run eeects, joint short and long-run eeects, heteroscedasticity and t-distributions are given using Monte Carlo methods. The MRR with the Bartlett window is generally robust with the disadvantage of a relatively small power. The trimmed Whittle likelihood has high power in general and is robust except for large short-run eeects. The tests are applied to changes in exchange rate series (daily data) of 6 major countries. The hypothesis of no fractional integration is rejected for none of the series. Acknowledgments: The author would like to thank two referees for valuable suggestions and A. Samarov for pointing to some relevant references.