Usually cointegration models involve a dynamic, stochastic component as well as deterministic components. This paper identifies relevant cotintegration models in terms of interpretability and similarity with respect to parameters of deterministic components. Similarity implies that inference on cointegration rank or common trends can be separated from inference on parameters of deterministic components. The idea is that the functional form and thereby the interpretation of deterministic components is not questioned in connection with the rank test, but it can be tested subsequently. The paper focuses on likelihood based inference in vector autoregressive models.