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On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests

Author

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  • Pierre Perron
  • Yohei Yamamoto
Abstract
Elliott and Müller (2006) considered the problem of testing for general types of parameter variations, including infrequent breaks. They developed a framework that yields optimal tests, in the sense that they nearly attain some local Gaussian power envelop. The main ingredient in their setup is that the variance of the process generating the changes in the parameters must go to zero at a fast rate. They recommended the so-called qLL test, a partial sums type test based on the residuals obtained from the restricted model. We show that for breaks that are very small, its power is indeed higher than other tests, including the popular sup-Wald test. However, the differences are very minor. When the magnitude of change is moderate to large, the power of the test is very low in the context of a regression with lagged dependent variables or when a correction is applied to account for serial correlation in the errors. In many cases, the power goes to zero as the magnitude of change increases. The power of the sup-Wald test does not show this non-monotonicity and its power is far superior to the qLL test when the break is not very small. We claim that the optimality of the qLL test does not come from the properties of the test statistics but the criterion adopted, which is not useful to analyze structural change tests. Instead, we use fixed-break size asymptotic approximations to assess the relative efficiency or power of the two tests. When doing so, it is shown that the sup-Wald test indeed dominates the qLL test and, in many cases, the latter has zero relative asymptotic efficiency.

Suggested Citation

  • Pierre Perron & Yohei Yamamoto, 2012. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Global COE Hi-Stat Discussion Paper Series gd12-258, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd12-258
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-258.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Yohei Yamamoto, 2018. "A modified confidence set for the structural break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(9), pages 974-999, October.
    2. Pierre Perron & Yohei Yamamoto, 2022. "Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 389-411, May.
    3. Seong Yeon Chang & Pierre Perron, 2018. "A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(6), pages 577-601, July.
    4. Alessandro Casini, 2018. "Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework," Papers 1803.10883, arXiv.org, revised Dec 2018.
    5. Pierre Perron & Yohei Yamamoto, 2021. "Testing for Changes in Forecasting Performance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 148-165, January.
    6. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    7. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    8. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    9. YAMAZAKI, Daisuke & 山崎, 大輔 & KUROZUMI, Eiji & 黒住, 英司, 2014. "Improving the Finite Sample Performance of Tests for a Shift in Mean," Discussion Papers 2014-16, Graduate School of Economics, Hitotsubashi University.
    10. HORIE, Tetsushi & 堀江, 哲史 & YAMAMOTO, Yohei & 山本, 庸平, 2016. "Testing for Speculative Bubbles in Large-Dimensional Financial Panel Data Sets," Discussion Papers 2016-04, Graduate School of Economics, Hitotsubashi University.

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    More about this item

    Keywords

    structural change; local asymptotics; Bahadur efficiency; hypothesis testing; parameter variations;
    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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