A Residual-Based ADF Test for Stationary Cointegration in I (2) Settings

• Authors: Javier Gómez Biscarri.
• BSE Working Paper: 110261 | September 15
• Keywords: systems , stationary cointegration , multicointegration , residual-based tests
• JEL codes: C12, C22, C32
• systems
• stationary cointegration
• multicointegration
• residual-based tests

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.