Test for long memory processes. A bootstrap approach
Many time series in diverse fields have been found to exhibit long memory. This paper analyzes the behavior of some of the most used tests for long memory: the R/S or rescaled R/S, the GPH (Geweke and Porter-Hudak) and the DFA (Detrended Fluctuation Analysis). Some of these tests exhibit size distortions in small-samples. It is well known that the bootstrap procedure may correct this fact. In this paper, size and power for those tests, for finite samples and different distributions such as normal, uniform and log-normal are investigated. In the case of short memory process, such as AR, MA and ARCH and long memory such as ARFIMA, p-values are calculated using the post-blackening, moving block bootstrap. The Monte Carlo studies suggest that the bootstrap critical values perform better. The results are applied to financial return time series.
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