Effect of Non-Normal Disturbances on Likelihood Ratio Tests

Since Granger (1981) first introduced the concept of cointegration the field has experienced a great development. There are by now several methods of estimating cointegrating vectors: Ordinary Least Squares (Engle and Granger (1987)), Non-linear Least Squares (Stock (1987)), Principal Components (Stock and Watson (1988)), Canonical Correlations (Bossaerts (1988)) and full information maximum likelihood in a Gaussian system (Johansen (1988b, 1991a)). All these methods of estimation are fairly simple to implement and this is probably why empirical applications grow in number very quickly. Inference, on the other hand, is more difficult to carry out. All known hypotheses tests on the number of cointegrating vectors have non standard asymptotic distributions. In addition, only the ML procedure1 allows the user to carry out inference on the cointegrating vectors and loading matrix based on standard χ2 tests.