Order selection in testing for the cointegrating rank of a VAR process

The impact of the choice of the lag length on tests for the number of cointegration relations in a vector autoregressive (VAR) process is investigated. It is shown that the asymptotic distribution of likelihood ratio (LR) tests for the cointegrating rank remains unchanged if the true data generation process (DGP) is of finite order and a consistent model selection criterion is used for choosing the lag length. A similar result also holds if the true DGP is an in finite order VAR. In a simulation study we find that small sample power and size of LR cointegration tests strongly depend on the choice of the lag order.