Computational Economics

, Volume 25, Issue 1–2, pp 103–113

Tests of Long Memory: A Bootstrap Approach


DOI: 10.1007/s10614-005-6277-6

Cite this article as:
Grau-Carles, P. Comput Econ (2005) 25: 103. doi:10.1007/s10614-005-6277-6


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 Geweke and Porter-Hudak (GPH) test and the detrended fluctuation analysis (DFA). Some of these tests exhibit size distortions in small samples. It is well known that the bootstrap procedure may correct this fact. Here I examine the size and power of those tests for finite samples and different distributions, such as the normal, uniform, and lognormal. In the short-memory processes such as AR, MA and ARCH and long memory ones such as 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.


long-memory tests bootstrap time series 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Departamento de Economía AplicadaUniversidad Rey Juan CarlosMadridSpain

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