We consider an m-dimensional vector autoregressive process Z_t of integratetd order 1, I(1), such that Z_t = (Y_t^',X_t^')^' where Y_t is an m_y-dimensional vector process of endogenous variables and X_t is an m_x-dimensional vector process of exogenous variables with m_y+ m_x = m. We assume that there are r cointegration relations in Z_t. Johansen (1992), Harbo et al. (1998), and Pesaran et al. (2000), considered inference of such process Z_t assuming the weak exogeneity of X_t, which in turn implies that the X_t is not cointegrated. In this paper, we consider the case where exogenous variables are cointegrated with rank r_x<m_x. Parameterization and estimation of this model are considered and the asymptotic properties of the least square estimator (LSE) and the maximum likelihood estimator (MLE) are presented. Parameterization in this paper can be easily applicable to the models considered in Mosconi and Gianni (1992) and Pradel and Rault (2003). The finite sample properties of the estimators are also examined through a Monte Carlo simulation. A real date example is presented to illustrate the methods.

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