The maximum likelihood estimator of the adjustment coefficient in a cointegrated vector autoregressive model (CVAR) is generally biased. For the case where the cointegrating vector is known in a first-order CVAR with no intercept, we derive a condition for the unbiasedness of the maximum...

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but of course the asymptotic results apply more generally....