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Assessing the Relative Power of Structural Break Tests Using a Framework Based on the Approximate Bahadur Slope

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  • Dukpa Kim

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  • Pierre Perron

    ()

Abstract

We compare the asymptotic relative efficiency of the Exp, Mean, and Sup functionals of the Wald, LM and LR tests for structural change analyzed by Andrews (1993) and Andrews and Ploberger (1994). We derive the approximate Bahadur slopes of these tests using large deviations techniques. These show that tests based on the Mean functional are inferior to those based on the Sup and Exp when using the same base statistic. Also, for a given functional, the Wald-based test dominates the LR-based test, which dominates the LM-based one. We show that the Sup and Mean type tests satisfy Wieand’s (1976) condition so that their slopes yield the limiting (as the size tends to zero) asymptotic relative Pitman efficiency. Using this measure of efficiency, the Mean type tests are also inferior to the Sup. We also compare tests based on the Wald and LM statistics modified with a HAC estimator. In this case, the inferiority of the LM-based tests is especially pronounced. The relevance of our theoretical results in finite samples is assessed via simulations. Our results are in contrast to those of Andrews and Ploberger (1994) based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems.

Suggested Citation

  • Dukpa Kim & Pierre Perron, 2006. "Assessing the Relative Power of Structural Break Tests Using a Framework Based on the Approximate Bahadur Slope," Boston University - Department of Economics - Working Papers Series WP2006-063, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2006-063
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    References listed on IDEAS

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    1. Deng, Ai & Perron, Pierre, 2008. "A non-local perspective on the power properties of the CUSUM and CUSUM of squares tests for structural change," Journal of Econometrics, Elsevier, vol. 142(1), pages 212-240, January.
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    14. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    15. Perron, Pierre & Vodounou, Cosme, 2005. "The Variance Ratio Test: An Analysis Of Size And Power Based On A Continuous-Time Asymptotic Framework," Econometric Theory, Cambridge University Press, vol. 21(03), pages 562-592, June.
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    Cited by:

    1. repec:eee:econom:v:204:y:2018:i:1:p:66-85 is not listed on IDEAS
    2. Luis Filipe Martins & Pierre Perron, 2016. "Improved Tests for Forecast Comparisons in the Presence of Instabilities," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(5), pages 650-659, September.
    3. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    4. 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.
    5. Seongyeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct to Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series 2013-023, Boston University - Department of Economics.
    6. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    7. Otilia Boldea & Alastair R. Hall, 2013. "Testing structural stability in macroeconometric models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 9, pages 206-228 Edward Elgar Publishing.
    8. Alessandro Casini, 2018. "Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework," Papers 1803.10883, arXiv.org.
    9. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    10. Kurozumi Eiji, 2015. "Testing for Multiple Structural Changes with Non-Homogeneous Regressors," Journal of Time Series Econometrics, De Gruyter, vol. 7(1), pages 1-35, January.
    11. Reese, Simon & Li, Yushu, 2013. "Testing for Structural Breaks in the Presence of Data Perturbations: Impacts and Wavelet Based Improvements," Working Papers 2013:36, Lund University, Department of Economics.
    12. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    13. PERRON, Pierre & YAMAMOTO, Yohei, 2018. "Testing for Changes in Forecasting Performance," Discussion Papers 2018-03, Graduate School of Economics, Hitotsubashi University.

    More about this item

    Keywords

    Change-Point; Hypothesis Testing; Unknown Break Date; Wald tests; Supremum statistics.;

    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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