Note on bandwidth selection in testing for long range dependence

Many tests for I(0) versus I(d) processes are standardized by long-run variance estimators, which are estimated by nonparametric methods that entail a choice of bandwidth. Data-dependent bandwidth choices using plug-in methods have been suggested and used in many applications. In a recent paper, Teverovsky et al. [Journal of Statistical Planning and Inference 80 (1999) 211] conducted a Monte Carlo study on the modified rescaled range (R/S) test and found that the test “has a strong bias towards accepting the null hypothesis”. In this note, we show that the Monte Carlo finding of unusually low power and the empirical finding of short-memory in stock returns indexes are related to the data-dependent bandwidth choice. Simply using the data-dependent bandwidth choice is inappropriate