Unit root testing under a local break in trend

David Harvey, Stephen Leybourne (steve.leybourne@nottingham.ac.uk) and Robert Taylor

Journal of Econometrics, 2012, vol. 167, issue 1, 140-167

Abstract: Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in both fixed trend break and no trend break environments, in finite samples pronounced “valleys” in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem, we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without-break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights.

Keywords: Unit root test; Local trend break; Union of rejections; Adaptive critical values; Asymptotic local power (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Related works:
Working Paper: Unit root testing under a local break in trend (2011)
Working Paper: Unit root testing under a local break in trend (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:167:y:2012:i:1:p:140-167

DOI: 10.1016/j.jeconom.2011.10.006

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