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Tests of Long Memory: A Bootstrap Approach

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  • Pilar Grau-Carles

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Abstract

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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Bibliographic Info

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

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: long-memory tests; bootstrap; time series;

References

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  1. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  2. Andersson, Michael K. & Gredenhoff, Mikael P., 1997. "Bootstrap Testing for Fractional Integration," Working Paper Series in Economics and Finance 188, Stockholm School of Economics.
  3. Xiao, Zhijie, 2003. "Note on bandwidth selection in testing for long range dependence," Economics Letters, Elsevier, vol. 78(1), pages 33-39, January.
  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. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
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Cited by:
  1. Murphy, A. & Izzeldin, M., 2009. "Bootstrapping long memory tests: Some Monte Carlo results," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2325-2334, April.
  2. A. Sensoy & Benjamin Miranda Tabak, 2013. "How much random does European Union walk? A time-varying long memory analysis," Working Papers Series 342, Central Bank of Brazil, Research Department.
  3. Hull, Matthew & McGroarty, Frank, 2014. "Do emerging markets become more efficient as they develop? Long memory persistence in equity indices," Emerging Markets Review, Elsevier, vol. 18(C), pages 45-61.
  4. Daniel Oliveira Cajueiro & Benjamin M. Tabak, 2010. "Fluctuation Dynamics in US Interest Rates and the Role of Monetary Policy," Working Papers Series 206, Central Bank of Brazil, Research Department.
  5. Eduardo Lima & Benjamin Tabak, 2009. "Tests of Random Walk: A Comparison of Bootstrap Approaches," Computational Economics, Society for Computational Economics, vol. 34(4), pages 365-382, November.
  6. Wang, Tiansong & Wang, Jun & Zhang, Junhuan & Fang, Wen, 2011. "Voter interacting systems applied to Chinese stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2492-2506.
  7. Belbute, José, 2013. "Does final demand for energy in Portugal exhibit long memory?," MPRA Paper 45717, University Library of Munich, Germany.

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