Unit Root Testing Using Covariates: Some Theory and Evidence
分析协变量增强迪基-富勒检验（CADF）相比传统ADF检验提高检验功效的条件，并证明该方法能避免单位根检验的尺寸扭曲，应用于美国宏观经济序列后推翻了多个序列存在单位根的结论。
This paper analyzes the conditions under which power gains can be achieved using the Covariate Augmented Dickey‐Fuller test (CADF) rather than the conventional Augmented Dickey‐Fuller (ADF), and argues that this method has the advantage, relative to univariate unit root tests, of increasing power without suffering from the large size distortions affecting the latter. The inclusion of covariates affects unit root testing by: (a) reducing the standard error of the estimate of the autoregressive parameter without affecting the estimate itself, and/or (b) reducing both the standard error and the absolute value of the estimate itself. Conditions in terms of contemporaneous correlation and Granger causality are derived for case (a) or (b) to arise. As an illustration, it is shown that applying the more powerful CADF (rather than the ADF) test reverses the finding of a unit root for many US macroeconomic series.