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A Modified Confidence Set for the Structural Break Date in Linear Regression Models

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  • Yamamoto, Yohei
  • 山本, 庸平

Abstract

Elliott and Müller (EM) (2007) provide a method for constructing a confidence set for the structural break date by inverting a variant of the locally best test statistic. Previous studies have shown that the EM method produces a set with an accurate coverage ratio even for a small break; however, the set is often overly lengthy. This study proposes a simple modification to rehabilitate their method through the long-run variance estimation. Following the literature, we provide an asymptotic justification for the improvement of the modified method over the original method under a nonlocal asymptotic framework. A Monte Carlo simulation shows that the modified method achieves a shorter confidence set than the EM method, especially when the break is large or the HAC correction is conducted. The modified method may exhibit minor errors in the coverage rate when the break is small; however, the coverage is more stable than alternative methods when the break is large. We apply our method to a level shift in post-1980s Japanese inflation data.
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Suggested Citation

  • Yamamoto, Yohei & 山本, 庸平, 2014. "A Modified Confidence Set for the Structural Break Date in Linear Regression Models," Discussion Papers 2014-08, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2014-08
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    References listed on IDEAS

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    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    6. 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.
    7. 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.
    8. Yamamoto, Yohei & Tanaka, Shinya, 2015. "Testing for factor loading structural change under common breaks," Journal of Econometrics, Elsevier, vol. 189(1), pages 187-206.
    9. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
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    Cited by:

    1. Eiji Kurozumi & Yohei Yamamoto, 2015. "Confidence sets for the break date based on optimal tests," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 412-435, October.
    2. Skrobotov, Anton, 2021. "Structural breaks in cointegration models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 63, pages 117-141.
    3. Yunjong Eo & James Morley, 2015. "Likelihood‐ratio‐based confidence sets for the timing of structural breaks," Quantitative Economics, Econometric Society, vol. 6(2), pages 463-497, July.
    4. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    5. KUROZUMI, Eiji & 黒住, 英司, 2017. "Confidence Sets for the Date of a Mean Shift at the End of a Sample," Discussion Papers 2017-06, Graduate School of Economics, Hitotsubashi University.
    6. Eiji Kurozumi & Anton Skrobotov, 2018. "Confidence Sets for the Break Date in Cointegrating Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(3), pages 514-535, June.

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    More about this item

    Keywords

    coverage ratio; nonlocal asymptotics; heteroskedasticity and autocorrelation consistent covariance; condence set;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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