Published online by Cambridge University Press: 12 December 2005
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.