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Testing for a Change in Mean under Fractional Integration

Author

Listed:
  • Iacone Fabrizio

    (Department of Economics and Related Studies, University of York, York, UK)

  • Leybourne Stephen J.

    (School of Economics and Granger Centre for Time Series Econometrics, University of Nottingham, Nottingham, UK)

  • Robert Taylor A.M.

    (Essex Business School, University of Essex, Colchester, UK)

Abstract

We consider testing for the presence of a change in mean, at an unknown point in the sample, in data that are possibly fractionally integrated, and of unknown order. This testing problem has recently been considered in a number of papers, most notably Shao (2011, “A Simple Test of Changes in Mean in the Possible Presence of Long-Range Dependence.” Journal of Time Series Analysis 32:598–606) and Iacone, Leybourne, and Taylor (2013b, “A Fixed-b Test for a Break in Level at an Unknown Time under Fractional Integration.” Journal of Time Series Analysis 35:40–54) who employ Wald-type statistics based on OLS estimation and rely on a self-normalization to overcome the fact that the standard Wald statistic does not have a well-defined limiting distribution across different values of the memory parameter. Here, we consider an alternative approach that uses the standard Wald statistic but is based on quasi-GLS estimation to control for the effect of the memory parameter. We show that this approach leads to significant improvements in asymptotic local power.

Suggested Citation

  • Iacone Fabrizio & Leybourne Stephen J. & Robert Taylor A.M., 2017. "Testing for a Change in Mean under Fractional Integration," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-8, January.
    • Handle: RePEc:bpj:jtsmet:v:9:y:2017:i:1:p:8:n:2
    DOI: 10.1515/jtse-2015-0006
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    References listed on IDEAS

    as
    1. Fabrizio Iacone & Stephen J. Leybourne & A. M. Robert Taylor, 2014. "A FIXED- b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 40-54, January.
    2. Iacone, Fabrizio & Leybourne, Stephen J. & Robert Taylor, A.M., 2013. "Testing for a break in trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 176(1), pages 30-45.
    3. Fabrizio Iacone, 2010. "Local Whittle estimation of the memory parameter in presence of deterministic components," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 37-49, January.
    4. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    5. Zhongjun Qu, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 423-438, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    2. Carina Gerstenberger, 2021. "Robust discrimination between long‐range dependence and a change in mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 34-62, January.
    3. Daiqing Xi & Tianxiao Pang, 2021. "Estimating multiple breaks in mean sequentially with fractionally integrated errors," Statistical Papers, Springer, vol. 62(1), pages 451-494, February.

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    More about this item

    Keywords

    change in mean; fractional integration; Wald statistic;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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