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Testing for a break in trend when the order of integration is unknown

Author

Listed:
  • Iacone, Fabrizio
  • Leybourne, Stephen J.
  • Robert Taylor, A.M.

Abstract

Harvey, Leybourne and Taylor [Harvey, D.I., Leybourne, S.J., Taylor, A.M.R. 2009. Simple, robust and powerful tests of the breaking trend hypothesis. Econometric Theory 25, 995–1029] develop a test for the presence of a broken linear trend at an unknown point in the sample whose size is asymptotically robust as to whether the (unknown) order of integration of the data is either zero or one. This test is not size controlled, however, when this order assumes fractional values; its asymptotic size can be either zero or one in such cases. In this paper we suggest a new test, based on a sup-Wald statistic, which is asymptotically size-robust across fractional values of the order of integration (including zero or one). We examine the asymptotic power of the test under a local trend break alternative. The finite sample properties of the test are also investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:30-45
    DOI: 10.1016/j.jeconom.2013.03.008
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    References listed on IDEAS

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    Cited by:

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    2. Jiawen Xu & Pierre Perron, 2013. "Robust testing of time trend and mean with unknown integration order errors Frequency (and Other) Contaminations," Boston University - Department of Economics - Working Papers Series 2013-006, Boston University - Department of Economics.
    3. Juan J. Dolado & Heiko Rachinger & Carlos Velasco, 2022. "LM Tests for Joint Breaks in the Dynamics and Level of a Long-Memory Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 629-650, April.
    4. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2018. "A simple test on structural change in long-memory time series," Economics Letters, Elsevier, vol. 163(C), pages 90-94.
    5. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    6. Seong Yeon Chang & Pierre Perron, 2017. "Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses," Econometrics, MDPI, vol. 5(1), pages 1-26, January.
    7. 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.
    8. 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.
    9. 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.
    10. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    11. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

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    More about this item

    Keywords

    Trend break; Fractional integration; Sup-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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