Break Date Estimation and Cointegration Testing in VAR Processes with Level Shift

In testing for the cointegrating rank of a vector autoregressive (VAR) process it is important to take into account level shifts that have occurred in the sample period. Therefore the properties of estimators of the time period where a shift has taken place are investigated. The possible structural break is modelled as a simple shift in the level of the process. Three alternative estimators for the break date are considered and their asymptotic properties are derived under various assumptions regarding the size of the shift. In particular, properties of the shift date estimator are obtained under the assumption of an increasing or decreasing size of the shift when the sample size grows. Moreover, the implications for testing the cointegrating rank of the process are explored. A new rank test is proposed and its asymptotic properties are derived. It is shown that its asymptotic null distribution is una®ected by the level shift. The performance of the shift date estimators and the cointegration rank tests in small samples is investigated by simulations.