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Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses

Author

Listed:
  • Mohitosh Kejriwal

    (Boston University, Department of Economics)

  • Pierre Perron

    (Boston University, Department of Economics)

Abstract
Perron (1989) introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and Andrews (1992), assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable for several reasons. First, it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing. Second, if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples.

Suggested Citation

  • Mohitosh Kejriwal & Pierre Perron, 2006. "Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses," Boston University - Department of Economics - Working Papers Series WP2006-052, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2006-052
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    structural change; pre-test; trend function; integrated processes; hypothesis testing.;
    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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