Testing for stationarity in a cointegrated system

In systems of variables with a specified or already identified cointegrating rank, stationarity of component variates can be tested by a simple restriction test. The implied decision is often in conflict with the outcome of unit root tests on the same variables. Using a framework of Bayes testing and decision contours, this paper searches for a solution to such conflict situations in sample sizes of empirical relevance. It evolves from the decision contour evaluations that the best test to be used jointly with a restriction test on self-cointegration is a modified version of the Dickey-Fuller test that accounts for the other system variables, whereas strictly univariate unit-root tests do not help much in the decision of interest.