Testing for the cointegrating rank of a VAR process with level shift at unknown time

A systems cointegration rank test is proposed which is applicable for vector autoregressive (VAR) processes with a structural shift at unknown time. The structural shift is modeled as a simple shift in the mean of the process. It is proposed to estimate the break date first on the basis of a full unrestricted VAR model. Two alternative estimators are considered and their asymptotic properties are derived. In the next step the deterministic part of the process including the shift size is estimated with a GLS procedure. Then the series are adjusted by subtracting the estimated deterministic part and a Johansen type test for the cointegrating rank is applied to the adjusted series. The test statistic is shown to have a well-known asymptotic null distribution which does not depend on the break date. The performance of the procedure in small samples is investigated by simulations. Finally, the procedure is applied for two sets of example series to illustrate its virtue for econometric analyses.