Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process

The properties of a range of maximum eigenvalue and trace tests for the coin-tegrating rank of a vector autoregressive process are compared. The tests are all likelihood-ratio-type tests and operate under different assumptions regarding the deterministic part of the data generation process. The asymptotic distributions under local alternatives are given and the local power is derived. It is found that the local power of corresponding maximum eigenvalue and trace tests is very similar. A Monte Carlo comparison shows, however, that there may be differences in small samples. The trace tests tend to have more distorted sizes whereas their power is in some situations superior to that of the maximum eigenvalue tests.