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Tests of Long Memory: A Bootstrap Approach

  • Pilar Grau-Carles

    ()

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. Copyright Springer Science + Business Media, Inc. 2005

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File URL: http://hdl.handle.net/10.1007/s10614-005-6277-6
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Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 25 (2005)
Issue (Month): 1 (February)
Pages: 103-113

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Handle: RePEc:kap:compec:v:25:y:2005:i:1:p:103-113
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100248

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  1. Xiao, Zhijie, 2003. "Note on bandwidth selection in testing for long range dependence," Economics Letters, Elsevier, vol. 78(1), pages 33-39, January.
  2. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
  3. Andersson, Michael K. & Gredenhoff, Mikael P., 1997. "Bootstrap Testing for Fractional Integration," SSE/EFI Working Paper Series in Economics and Finance 188, Stockholm School of Economics.
  4. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
  5. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M. 96a15, Universite Aix-Marseille III.
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