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A test of the long memory hypothesis based on self-similarity

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  • James Davidson
  • Dooruj Rambaccussing

Abstract

This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skip-sampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of signi cance of the long memory parameter, and a composite test procedure is described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependent-sample bootstrap technique to approximate short-run dependence following fractional di¤erencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.

Suggested Citation

  • James Davidson & Dooruj Rambaccussing, 2015. "A test of the long memory hypothesis based on self-similarity," Dundee Discussion Papers in Economics 286, Economic Studies, University of Dundee.
  • Handle: RePEc:dun:dpaper:286
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    File URL: http://www.dundee.ac.uk/media/dundeewebsite/economicstudies/documents/discussion/DDPE_286.pdf
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    References listed on IDEAS

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    1. Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(04), pages 724-731, October.
    2. Davidson, James & Hashimzade, Nigar, 2009. "Type I and type II fractional Brownian motions: A reconsideration," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2089-2106, April.
    3. Jon Faust, 1999. "Conventional Confidence Intervals for Points on Spectrum Have Confidence Level Zero," Econometrica, Econometric Society, vol. 67(3), pages 629-638, May.
    4. Leonardo Rocha Souza, 2005. "A Note On Chambers'S "Long Memory And Aggregation In Macroeconomic Time Series"," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 1059-1062, August.
    5. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    6. repec:hal:journl:peer-00815563 is not listed on IDEAS
    7. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
    8. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 475-495.
    9. Souza, Leonardo R. & Smith, Jeremy, 2002. "Bias in the memory parameter for different sampling rates," International Journal of Forecasting, Elsevier, vol. 18(2), pages 299-313.
    10. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
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    Cited by:

    1. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.

    More about this item

    Keywords

    Long Memory; Self-similarity; Bootstrap;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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