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A Comparison of Alternative Methods to Construct Confidence Intervals for the Estimate of a Break Date in Linear Regression Models

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  • Seong Yeon Chang

    () (Xiamen University)

  • Pierre Perron

    () (Boston University)

Abstract

This paper considers constructing conÖdence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the per- formance of various procedures in terms of exact coverage rates and lengths of the conÖdence intervals. These include the procedures of Bai (1997) based on the asymp- totic distribution under a shrinking shift framework, Elliott and Muller (2007) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Muller's (2007) approach is by far the best one. However, this comes with a very high cost in terms of the length of the conÖdence intervals. When the errors are se- rially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal to noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Muller's (2007) method.

Suggested Citation

  • Seong Yeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series wp2015-010, Boston University - Department of Economics, revised 11 Oct 2015.
  • Handle: RePEc:bos:wpaper:wp2015-010
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    References listed on IDEAS

    as
    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. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(03), pages 335-347, September.
    3. Yohei Yamamoto & Pierre Perron, 2013. "Estimating and testing multiple structural changes in linear models using band spectral regressions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 400-429, October.
    4. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    5. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    6. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    7. Perron, Pierre & Yamamoto, Yohei, 2014. "A Note On Estimating And Testing For Multiple Structural Changes In Models With Endogenous Regressors Via 2sls," Econometric Theory, Cambridge University Press, vol. 30(02), pages 491-507, April.
    8. 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.
    9. Perron, P., 1991. "A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series," Papers 363, Princeton, Department of Economics - Econometric Research Program.
    10. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    11. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-162, April.
    12. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    13. 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.
    14. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
    15. Graham Elliott & Ulrich K. Muller, 2006. "Efficient Tests for General Persistent Time Variation in Regression Coefficients," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 907-940.
    16. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    17. 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.
    18. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
    19. 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.
    20. Alberto Musso & Livio Stracca & Dick van Dijk, 2009. "Instability and Nonlinearity in the Euro-Area Phillips Curve," International Journal of Central Banking, International Journal of Central Banking, vol. 5(2), pages 181-212, June.
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    Cited by:

    1. repec:taf:emetrv:v:37:y:2018:i:9:p:974-999 is not listed on IDEAS
    2. Skrobotov Anton & Eiji Kurozumi, 2016. "Confidence Sets for the Break Date in Cointegrating Regressions," Working Papers wpaper-2016-268, Gaidar Institute for Economic Policy, revised 2016.
    3. Otilia Boldea & Alastair R. Hall & Adriana Cornea-Madeira, 2017. "Bootstrapping Structural Change Tests," The School of Economics Discussion Paper Series 1704, Economics, The University of Manchester.
    4. 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.
    5. 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.
    6. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.

    More about this item

    Keywords

    Bootstrap; Confidence interval; Dynamic regression models; Inverted likelihood ratio; Non-monotonic power; Serially correlated errors; Structural change;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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