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, \textit{V. Teverovsky}, \textit{M. S. Taqqu} and \textit{W. Willinger} [J. Stat. Plann. Inference 80, 211--227 (1999; Zbl 1044.60508)] 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.
scientific article; zbMATH DE number 1857191