The finite sample properties of three semiparametric estimators, several versions of the modified rescaled range, MMR, and three versions of the GHURST estimator are investigated. Their power and size for testing for long memory under short-run effects, joint short and long-run effects, heteroscedasticity and t-distributions are given using Monte Carlo methods. The MMR with the Barlett window is generally robust with the disadvantage of a relatively small power. The trimmed Whittle likelihood has high power in general and is robust expect for large short-run effects. The tests are applied to chandes in exchange rate series (daily data) of 6 major countries. The hypothesis of no fractional integration is rejected for none of the series. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing