Testing cointegration in infinite order vector autoregressive processes

This paper studies test procedures which can be used to determine the cointegrating rank in infinite order vector autoregressive processes. The considered tests are analogs or close versions of previous likelihood ratio tests obtained for finite-order Gaussian vector autoregressive processes. It is shown that the use of the likelihood ratio tests is justified even when the data are generated by an infinite order non-Gaussian vector autoregressive process. New tests are also developed for cases where intercept terms are included in the cointegrating relations. These tests are based on a new approach of estimating the intercept terms. They have the property that, under the null hypothesis, the same asymptotic distribution theory applies as in the case where the values of the intercept terms are a priori known and not estimated. A limited simulation study indicates that the new tests can be considerably more powerful than their previous counterparts.