Bootstrapping long memory tests: Some Monte Carlo results
Computational Statistics & Data Analysis
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Many time series in diverse fields of application may exhibitlong-memory. The class of fractionally integrated (FI) processescan be used to try to model this strong data dependence. Asymptotictests for FI include the re-scaled range statistic test and itsmodified form, the frequency-domain regression-based procedure, themodified Higuchi's test and Jensen's test. De Peretti andMarimoutou (2002) finds that proper finite-sample inferences arenot possible using these techniques without correcting for sizedistortions. Some attempt this correction through 'bootstrapping',but this method is not perfect and needs more study andimprovements. In this paper, I examine and compare thefinite-sample properties of parametric and nonparametric bootstraptests by using graphical techniques of Davidson and MacKinnon(1998a) for showing whether they properly correct the distortionswhile retaining their power relative to the correspondingasymptotic tests. One of the tests uses a double bootstrap thatprovide better true power and size properties. I use a bilateral Pvalue that permits the true power of the tests to grow when thesize distortions are asymmetric. We then apply these procedures toa real time series to investigate its long memory properties.