Tests of Long Memory: A Bootstrap Approach”, Computational conomics

Many time series in diverse fields have been found to exhibit long memory. This paper analyzes the behaviour of some of the most used tests of long memory: the R/S analysis, the modified R/S, the GPH (Geweke and Porter-Hudak) test 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 lognormal are investigated. In the case of short memory processes such as AR, MA and ARCH and long memory such ARFIMA, p-values are calculated using the post-blackening moving block bootstrap. The Monte Carlo study suggests that the bootstrap critical values perform better. The results are applied to financial return time series.