Testing for Cointegration in Multivariate Time Series : An evaluation of the Johansens trace test and three different bootstrap tests when testing for cointegration

Sammanfattning: In this paper we examine, by Monte Carlo simulation, size and power of the Johansens trace test when the error covariance matrix is nonstationary, and we also investigate the properties of three different bootstrap cointegration tests. Earlier studies indicate that the Johansen trace test is not robust in presence of heteroscedasticity, and tests based on resampling methods have been proposed to solve the problem. The tests that are evaluated is the Johansen trace test, nonparametric bootstrap test and two different types of wild bootstrap tests. The wild bootstrap test is a resampling method that attempts to mimic the GARCH model by multiplying each residual by a stochastic variable with an expected value of zero and unit variance. The wild bootstrap tests proved to be superior to the other tests, but not as good as earlier indicated. The more the error terms differs from white noise, the worse these tests are doing. Although the wild bootstrap tests did not do a very bad job, the focus of further investigation should be to derive tests that does an even better job than the wild bootstrap tests examined here.