### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 1196-1218 |

Number of pages | 23 |

Journal | Journal of Econometrics |

Volume | 141 |

Issue number | 2 |

DOIs | |

State | Published - Dec 2007 |

### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Keywords

- Coverage control
- Locally best test
- Test inversion

## Fingerprint Dive into the research topics of 'Confidence sets for the date of a single break in linear time series regressions'. Together they form a unique fingerprint.

## Cite this

*Journal of Econometrics*,

*141*(2), 1196-1218. https://doi.org/10.1016/j.jeconom.2007.02.001