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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.

Suggested Citation

  • Elliott, Graham & Muller, Ulrich K., 2004. "Confidence Sets for the Date of a Single Break in Linear Time Series Regressions," University of California at San Diego, Economics Working Paper Series qt9hf4j4c2, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt9hf4j4c2
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