Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term

When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to being orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare three alternative procedures, which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects, in the second one the trend term is decided upon by a pretest and in the third procedure only tests which allow for an unrestricted trend term are used. We provide theoretical asymptotic and small sample simulation results, which show that the first strategy is preferable in applied work.