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On infimum Dickey–Fuller unit root tests allowing for a trend break under the null

Harvey, David I.; Leybourne, Stephen J.; Taylor, A.M. Robert

Authors

David I. Harvey

Stephen J. Leybourne

A.M. Robert Taylor



Abstract

Trend breaks appear to be prevalent in macroeconomic time series. Consequently, to avoid the catastrophic impact that unmodelled trend breaks have on power, it is standard empirical practice to employ unit root tests which allow for such effects. A popularly applied approach is the infimum ADF-type test. Its appeal has endured with practitioners despite results which show that the infimum ADF statistic diverges to −∞−∞ as the sample size diverges, with the consequence that the test has an asymptotic size of unity when a break in trend is present under the unit root null hypothesis. The result for additive outlier-type breaks in trend (but not intercept) is refined and shows that divergence to −∞−∞ occurs only when the true break fraction is smaller than 2/32/3. An alternative testing strategy based on the maximum of the original infimum statistic and the corresponding statistic constructed using the time-reversed sample data is considered.

Journal Article Type Article
Publication Date Jan 1, 2014
Journal Computational Statistics & Data Analysis
Electronic ISSN 1872-7352
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 78
APA6 Citation Harvey, D. I., Leybourne, S. J., & Taylor, A. R. (2014). On infimum Dickey–Fuller unit root tests allowing for a trend break under the null. Computational Statistics and Data Analysis, 78, doi:10.1016/j.csda.2012.10.017
DOI https://doi.org/10.1016/j.csda.2012.10.017
Keywords Unit root test; Trend break; Minimum Dickey–Fuller test
Publisher URL http://www.sciencedirect.com/science/article/pii/S0167947312003854
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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