This paper considers a semi-nonparametric cointegration test. The test uses the LM-testing principle. The score function needed for the LM-test is estimated from the data using an expansion of the density around a Student t distribution. In this way, we capture both the possible fat-tailedness and the skewness of the innovation process. Using a Monte Carlo experiment, we show that the semi-nonparametric cointegration test has good size and power properties over a broad class of distributions for the innovation process. We also investigate the effect of order selection of the underlying VAR on inference. The complete methodology is illustrated using an interest rate example. © 2002 Elsevier Science B.V. All rights reserved.