Lucas, A. (1998). Inference on cointegrating ranks using lr and lm tests based on pseudo-likelihoods Econometric Reviews, 17(2):185--214.

This paper considers Lagrange Multiplier (LM) and Likelihood Ratio (LR) tests for determining the cointegrating rank of a vector autoregressive system. n order to deal with outliers and possible fat-tailedness of the error process, non-Gaussian likelihoods are used to carry out the estimation. The limiting distributions of the tests based on these non-Gaussian pseudo-)likelihoods are derived. These distributions depend on nuisance parameters. An operational procedure is proposed to perform inference. It appears that the tests based on non-Gaussian pseudo-likelihoods are much more powerful than their Gaussian counterparts if the errors are fat-tailed. Moreover, the operational LM-type test has a better overall performance than the LR-type test. Copyright O 1998 by Marcel Dekker, Inc.