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A test of long memory hypothesis based on self-similarity

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  • Rambaccussing, Dooruj
  • Davidson, James

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 significance of the long memory parameter, and composite test procedure 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 differencing. 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

  • Rambaccussing, Dooruj & Davidson, James, 2015. "A test of long memory hypothesis based on self-similarity," SIRE Discussion Papers 2015-81, Scottish Institute for Research in Economics (SIRE).
    • Handle: RePEc:edn:sirdps:689
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    File URL: http://hdl.handle.net/10943/689
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    References listed on IDEAS

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    7. Benedikt M. Poetscher, 2002. "Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parame," Econometrica, Econometric Society, vol. 70(3), pages 1035-1065, May.
    8. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    9. 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.
    10. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    11. Chambers, Marcus J, 1998. "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. 39(4), pages 1053-1072, November.
    12. 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.
    13. 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.
    14. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    15. Souza, Leonardo R. & Smith, Jeremy, 2004. "Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study," International Journal of Forecasting, Elsevier, vol. 20(3), pages 487-502.
    16. 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.
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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.
    2. Less, Vivien & Sibbertsen, Philipp, 2022. "Estimation and Testing in a Perturbed Multivariate Long Memory Framework," Hannover Economic Papers (HEP) dp-704, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    3. Ata Assaf & Luis Alberiko Gil-Alana & Khaled Mokni, 2022. "True or spurious long memory in the cryptocurrency markets: evidence from a multivariate test and other Whittle estimation methods," Empirical Economics, Springer, vol. 63(3), pages 1543-1570, September.
    4. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    5. Dooruj Rambaccussing & Murat Mazibas, 2020. "True versus Spurious Long Memory in Cryptocurrencies," JRFM, MDPI, vol. 13(9), pages 1-11, August.
    6. Yixun Xing & Wayne A. Woodward, 2021. "R-Squared-Bootstrapping for Gegenbauer-Type Long Memory," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 773-790, February.
    7. Walid Chkili, 2021. "Modeling Bitcoin price volatility: long memory vs Markov switching," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(3), pages 433-448, September.

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    More about this item

    Keywords

    long memory; self-similarity; bootstrap;
    All these keywords.

    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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