Comparison of tests for the cointegrating rank of a VAR process with a structural shift

Two different types of tests for the cointegrating rank of VAR processes with a deterministic shift in the level have been proposed in the literature. The first proposal is based on the LR principle using a specific Gaussian model set-up. In the second proposal the time series are adjusted for deterministic terms first and then LR type tests are applied to the adjusted series. The local power of the two types of tests is derived and compared. Moreover, the small sample size and power properties of the tests are explored. It is found that the tests based on adjusted series generally have superior local power and size properties.