Break Date Estimation For Var Processes With Level Shift With An Application To Cointegration Testing

In testing for the cointegrating rank of a vector autoregressive 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 modeled as a simple shift in the level of the process. Two 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 estimators are obtained under the assumption of an increasing or decreasing size of the shift when the sample size grows. These results are used to explore the implications for testing the cointegrating rank of the process. A previously proposed likelihood ratio type test for the cointegrating rank and a modified version are considered, and their asymptotic properties are derived. It is shown that their asymptotic null distributions are unaffected by the level shift under the assumptions made for the shift size. The performance of the shift date estimators and the cointegrating rank tests in small samples is investigated by simulations.We thank two referees for helpful comments, and we are grateful to the Deutsche Forschungsgemeinschaft, SFB 373, and the European Commission under the Training and Mobility of Researchers Programme (contract ERBFMRXCT980213) for financial support. The first author also acknowledges financial support by the Yrjö Jahnsson Foundation, the Academy of Finland, and the Alexander von Humboldt Foundation under a Humboldt research award. Part of this research was done while he was visiting the Humboldt University in Berlin, and part of the research was carried out while he and the third author were visiting the European University Institute, Florence. An extended version of this paper is available as an EUI discussion paper under the title “Break Date Estimation and Cointegration Testing in VAR Processes with Level Shift,” ECO 2004/21.