The impact of the initial condition on covariate augmented unit root tests
Aristidou, Chrystalleni and Harvey, David I. and Leybourne, Stephen J. (2016) The impact of the initial condition on covariate augmented unit root tests. Journal of Time Series Econometrics . ISSN 1941-1928
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.
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