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Unit root testing under a local break in trend

Author

Listed:
  • David I. Harvey
  • Stephen J. Leybourne
  • A. M. Robert Taylor

Abstract

Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in bothfixed trend break and no trend break environments, in finite samples pronounced “valleys" in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights.

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2011. "Unit root testing under a local break in trend," Discussion Papers 11/02, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:11/02
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    File URL: http://www.nottingham.ac.uk/research/groups/grangercentre/documents/11-02.pdf
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Anton Skrobotov, 2013. "Local Structural Trend Break in Stationarity Testing," Working Papers 0074, Gaidar Institute for Economic Policy, revised 2013.
    2. Skrobotov Anton, 2018. "On Trend Breaks and Initial Condition in Unit Root Testing," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-15, January.
    3. Skrobotov, Anton (Скроботов, Антон), 2015. "About Trend, the Shift and the Initial Value in Testing of the Hypothesis of a Unit Root
      [О Тренде, Сдвиге И Начальном Значении В Тестировании Гипотезы О Наличии Единичного Корня]
      ," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.
    4. Neil Kellard & Denise Osborn & Jerry Coakley & Giuseppe Cavaliere & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2015. "Testing for Unit Roots Under Multiple Possible Trend Breaks and Non-Stationary Volatility Using Bootstrap Minimum Dickey–Fuller Statistics," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 603-629, September.
    5. Anton Skrobotov, 2014. "A simple modification of the Busetti-Harvey stationarity tests with structural breaks at unknown time," Working Papers 0102, Gaidar Institute for Economic Policy, revised 2014.
    6. repec:eee:ecosta:v:4:y:2017:i:c:p:70-90 is not listed on IDEAS
    7. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2013. "Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics," Journal of Econometrics, Elsevier, vol. 177(2), pages 265-284.

    More about this item

    Keywords

    Unit root test; local trend break; union of rejections; adaptive critical values; asymptotic local power;

    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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