The Impact of the Initial Condition on Covariate Augmented Unit Root Tests

Aristidou Chrystalleni, David Harvey and Stephen Leybourne ()
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Aristidou Chrystalleni: School of Economics, University of Nottingham, Nottingham, United Kingdom of Great Britain and Northern Ireland

Journal of Time Series Econometrics, 2017, vol. 9, issue 1, 23

Abstract: We examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.” Econometric Theory 11:1148–71) and Elliott and Jansson (2003, “Testing for Unit Roots with Stationary Covariates.” Journal of Econometrics 115:75–89), respectively, in situations where the magnitude of the initial condition of the time series under consideration may be non-negligible. We show that the asymptotic power of such tests is very sensitive to the initial condition; OLS- and GLS-based tests achieve relatively high power for large and small magnitudes of the initial condition, respectively. Combining information from both types of test via a simple union of rejections strategy is shown to effectively capture the higher power available across all initial condition magnitudes.

Keywords: Unit root tests; stationary covariates; initial condition uncertainty; asymptotic power (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2017
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Working Paper: The impact of the initial condition on covariate augmented unit root tests (2016)
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DOI: 10.1515/jtse-2015-0013

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