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

Graham Elliott, Ulrich K. Müller

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This paper considers 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 the current standard method in econometrics for constructing such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that breaks of moderate magnitude are a theoretically and empirically relevant phenomenon, we proceed to develop an appropriate alternative. We suggest constructing confidence sets by inverting a sequence of tests. Each of the tests maintains a specific break date under the null hypothesis, and rejects when a break occurs elsewhere. By inverting a certain variant of a 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.

Original languageEnglish (US)
Pages (from-to)1196-1218
Number of pages23
JournalJournal of Econometrics
Issue number2
StatePublished - Dec 2007

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Coverage control
  • Locally best test
  • Test inversion


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