Testing the Cointegrating Rank with Uncorrelated but Dependent Errors

Abstract

We study the asymptotic behavior of the reduced rank estimator of the cointegrating space and adjustment space for vector error correction time series models with nonindependent innovations. It is shown that the distribution of the adjustment space can be quite different for models with iid innovations and models with nonindependent innovations. It is also shown that the likelihood ratio test remains valid when the assumption of iid Gaussian errors is relaxed. Monte Carlo experiments illustrate the finite sample performance of the likelihood ratio test using various kinds of weak error processes.