A residual-based ADF test for stationary cointegration in settings

We propose a residual-based augmented Dickey–Fuller (ADF) test statistic that allows for detection of stationary cointegration within a system that may contain both I ( 2 ) and I ( 1 ) observables. The test is also consistent under the alternative of multicointegration, where first differences of the I ( 2 ) observables enter the cointegrating relationships. We find the null limiting distribution of this statistic and justify why our proposal improves over related approaches. Critical values are computed for a variety of situations. Additionally, building on this ADF test statistic, we propose a procedure to test the null of no stationary cointegration which overcomes the drawback, suffered by any residual-based method, of the lack of power with respect to some relevant alternatives. Finally, a Monte Carlo experiment is carried out and an empirical application is provided as an illustrative example.