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.

中文翻译：

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初始条件对协变量增强单位根检验的影响

摘要我们研究了采用平稳协变量的，经过OLS降级/去趋势化和GLS降级/去趋势化的单位根检验的行为，这是由Hansen（1995年，“重新思考单位根检验的单变量方法”。）计量经济学理论11：1148–71 ）和Elliott和Jansson（2003年，“用平稳协变量测试单位根”。《计量经济学杂志》 115：75-89），在所考虑的时间序列的初始条件的大小可能不可忽略的情况下。我们证明了这种测试的渐近能力对初始条件非常敏感。基于OLS和GLS的测试分别针对较大和较小量的初始条件实现了相对较高的功率。