Testing for the Cointegrating Rank of a Vector Autoregressive Process with Uncertain Deterministic Trend Term

Abstract

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 be 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 two alternative testing strategies 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 and in the second one the trend term is decided upon by a pretest. The first strategy is shown to be preferable in applied work.Cointegration analysis, likelihood ratio test, vector autoregressive model, vector error correction model