A comparison of parametric, semi-nonparametric, adaptive and nonparametric tests

This paper provides an extensive Monte-Carlo comparison of several contemporary cointegration tests. Apart from the familiar Gaussian based tests of Johansen, we also consider tests based on non-Gaussian quasi-likelihoods. Moreover, we compare the performance of these parametric tests with tests that estimate the score function from the data using either kernel estimation or semi-nonparametric density approximations. The comparison is completed with a fully nonparametric cointegration test. In small samples, the overall performance of the semi-nonparametric approach appears best in terms of size and power. The main cost of the semi-nonparametric approach is the increased computation time. In large samples and for heavily skewed or multimodal distributions, the kernel based adaptive method dominates. For near-Gaussian distributions, however, the semi-nonparametric approach is preferable again.