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Confidence sets for the date of a single break in linear time series regressions

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  • Elliott, Graham
  • Muller, Ulrich K.

Abstract

We consider the problem of constructing confidence sets for the date of a single break in a linear time series regression. We establish analytically and by small sample simulation that he currently standard method in econometrics to construct such intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that such breaks are a theoretically and empirically highly relevant phenomenon, we proceed to develop an appropriate alternative. We suggest constructing confidence sets by inverting a sequence of tests. Each test maintains a specific break date under the null hypothesis, and rejects when a break occurs elsewhere. By inverting a certain variant of a modified locally best invariant test, we ensure that the asymptotic critical value does not depend on the maintained break date. A valid confidence set can hence be obtained by assessing which of the sequence of test statistics exceeds a single number.
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  • 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.
  • Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:1196-1218
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    Cited by:

    1. Brian Chi-ang Lin & Siqi Zheng & Felix Pretis & Lea Schneider & Jason E. Smerdon & David F. Hendry, 2016. "Detecting Volcanic Eruptions In Temperature Reconstructions By Designed Break-Indicator Saturation," Journal of Economic Surveys, Wiley Blackwell, vol. 30(3), pages 403-429, July.
    2. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, Elsevier.
    3. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    4. Yamamoto, Yohei, 2014. "A Modified Confidence Set for the Structural Break Date in Linear Regression Models," Discussion Papers 2014-08, Graduate School of Economics, Hitotsubashi University.
    5. González-Rivera, Gloria & Sun, Yingying, 2017. "Density forecast evaluation in unstable environments," International Journal of Forecasting, Elsevier, vol. 33(2), pages 416-432.
    6. Tom Boot & Andreas Pick, 2017. "A near optimal test for structural breaks when forecasting under square error loss," Tinbergen Institute Discussion Papers 17-039/III, Tinbergen Institute.
    7. José Manuel Campa & Linda S. Goldberg & José M. González-Mínguez, 2005. "Exchange-Rate Pass-Through to Import Prices in the Euro Area," NBER Working Papers 11632, National Bureau of Economic Research, Inc.
    8. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany.
    9. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    10. Linda S. Goldberg & Michael W. Klein, 2005. "Establishing Credibility: Evolving Perceptions of the European Central Bank," NBER Working Papers 11792, National Bureau of Economic Research, Inc.
    11. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408 Edward Elgar Publishing.
    12. Alessandro Casini & Pierre Perron, 2015. "Continuous Record Asymptotics for Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-010, Boston University - Department of Economics, revised Nov 2017.
    13. KUROZUMI, Eiji, 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.
    14. Alessandro Casini & Pierre Perron, 2017. "Continuous Record Laplace-based Inference about the Break Date in Structural Change Models," Boston University - Department of Economics - Working Papers Series WP2018-011, Boston University - Department of Economics.
    15. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    16. Harvey, David I. & Leybourne, Stephen J., 2015. "Confidence sets for the date of a break in level and trend when the order of integration is unknown," Journal of Econometrics, Elsevier, vol. 184(2), pages 262-279.
    17. Elliott, Graham & Müller, Ulrich K., 2014. "Pre and post break parameter inference," Journal of Econometrics, Elsevier, vol. 180(2), pages 141-157.
    18. Harvey, David I. & Leybourne, Stephen J., 2016. "Improving the length of confidence sets for the date of a break in level and trend when the order of integration is unknown," Economics Letters, Elsevier, vol. 145(C), pages 239-245.

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