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Confidence Sets for the Date of a Single Break in Linear Time Series Regressions

  • Elliott, Graham
  • Muller, Ulrich K.
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    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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    File URL: http://www.escholarship.org/uc/item/9hf4j4c2.pdf;origin=repeccitec
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    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt9hf4j4c2.

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    Date of creation: 01 Aug 2004
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    Handle: RePEc:cdl:ucsdec:qt9hf4j4c2
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    1. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
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