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

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Author Info
Graham Elliott (University of California, San Diego)
Ulrich Muller (Princeton University)

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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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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2004-10.

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Date of creation: 29 Sep 2004
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Handle: RePEc:cdl:ucsdec:2004-10

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Related research
Keywords: Test Inversion; Coverage Control; Locally Best Test;

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  2. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 10372, University Library of Munich, Germany. [Downloadable!]
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  6. Eo, Yunjong & Morley, James C., 2008. "Likelihood-Based Confidence Sets for the Timing of Structural Breaks," MPRA Paper 13913, University Library of Munich, Germany. [Downloadable!]
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