Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

Dukpa Kim, Pierre Perron

Research output: Contribution to journalArticle

157 Citations (Scopus)

Abstract

Perron [Perron, P., 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361-1401] introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and Andrews [Zivot, E., Andrews, D.W.K., 1992. Further evidence on the great crash, the oil price shock and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251-270], assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable since (a) it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing; (b) if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of Econometrics
Volume148
Issue number1
DOIs
Publication statusPublished - 2009 Jan 1
Externally publishedYes

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Unit Root Tests
Null
Unknown
Date
Alternatives
Testing
Unit Root
Crash
Shock
Time series
Valid
Statistics
Limit Distribution
Stationarity
Economics
Small Sample
Simulation Experiment
Slope
Trends
Unit root tests

Keywords

  • Hypothesis testing
  • Integrated processes
  • Pre-test
  • Structural change
  • Trend function

ASJC Scopus subject areas

  • History and Philosophy of Science
  • Economics and Econometrics
  • Applied Mathematics

Cite this

Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses. / Kim, Dukpa; Perron, Pierre.

In: Journal of Econometrics, Vol. 148, No. 1, 01.01.2009, p. 1-13.

Research output: Contribution to journalArticle

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