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Testing For Long Memory

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  • Harris, David
  • McCabe, Brendan
  • Leybourne, Stephen

Abstract

This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.

Suggested Citation

  • Harris, David & McCabe, Brendan & Leybourne, Stephen, 2008. "Testing For Long Memory," Econometric Theory, Cambridge University Press, vol. 24(1), pages 143-175, February.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:01:p:143-175_08
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    Cited by:

    1. Bill Russell & Dooruj Rambaccussing, 2016. "Breaks and the Statistical Process of Inflation: The Case of the ‘Modern’ Phillips Curve," Dundee Discussion Papers in Economics 294, Economic Studies, University of Dundee.
    2. Bill Russell & Dooruj Rambaccussing, 2019. "Breaks and the statistical process of inflation: the case of estimating the ‘modern’ long-run Phillips curve," Empirical Economics, Springer, vol. 56(5), pages 1455-1475, May.
    3. Piotr Płuciennik, 2012. "The Impact of the World Financial Crisis on the Polish Interbank Market: A Swap Spread Approach," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(4), pages 269-288, December.
    4. Amsler Christine & Schmidt Peter, 2012. "A Comparison of the Robustness of Several Tests of Short Memory to Autocorrelated Errors," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 56-66, August.
    5. Kuswanto, Heri & Sibbertsen, Philipp, 2009. "Testing for Long Memory Against ESTAR Nonlinearities," Hannover Economic Papers (HEP) dp-427, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. repec:lan:wpaper:3329 is not listed on IDEAS
    7. repec:lan:wpaper:3053 is not listed on IDEAS
    8. Georgios P. Kouretas & Mark E. Wohar, 2012. "The dynamics of inflation: a study of a large number of countries," Applied Economics, Taylor & Francis Journals, vol. 44(16), pages 2001-2026, June.
    9. Granville, Brigitte & Zeng, Ning, 2019. "Time variation in inflation persistence: New evidence from modelling US inflation," Economic Modelling, Elsevier, vol. 81(C), pages 30-39.
    10. Castano Vélez, Elkin & Gallón Gómez, Santiago Alejandro & Gómez Portilla, Karoll, 2011. "Sesgos en estimación, tamano y potencia de una prueba sobre el parámetro de memoria larga en modelos ARFIMA," Revista Lecturas de Economía, Universidad de Antioquia, CIE, February.
    11. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    12. repec:lan:wpaper:3051 is not listed on IDEAS
    13. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    14. 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.
    15. Ning Zeng, 2015. "Monetary Stability and Stock Returns: A Bivariate Generalized Autoregressive Conditional Heteroscedasticity Modelling Study," Business and Economic Research, Macrothink Institute, vol. 5(2), pages 1-22, December.
    16. Elkin Castaño & Santiago Gallón & Karoll Gómez, 2010. "Estimation Biases, Size and Power of a Test on the Long Memory Parameter in ARFIMA Models," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 73, pages 131-148.
    17. repec:lan:wpaper:3145 is not listed on IDEAS

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