This book gives a detailed mathematical and statistical analysis of the cointegrated vector autoregresive model. This model had gained popularity because it can at the same time capture the short-run dynamic properties as well as the long-run equilibrium behaviour of many non-stationary time series. It also allows relevant economic questions to be formulated in a consistent statistical I of the book is planned so that it can beused by those who want to apply the methods without going into too much detail about the probability theory. The main emphasis is on the derivation of estimators and test statistics through a consistentuse of the Guassian likelihood function. It is shown that many different models can be formulated within the framework of the autoregressive model and the interpretation of these models is discussed in detail. In particular, models involving restrictions on the cointegration vectors and the adjustment coefficients are discussed, as well as the role of the constant and linear Part II, the asymptotic theory is given the slightly more general framework of stationarylinear processes with i.i.d. innovations. Some useful mathematical tools are collected in Appendix A, and a brief summary of weak convergence in given in Appendix book isintended to give a relatively self-contained presentation for graduate students and researchers with a good knowledge of multivariate regression analysis and likelihood methods. The asymptotic theory requires some familiarity with the theory of weak convergence of stochastic processes. The theory is treated in detail with the purpose of giving the reader a working knowledge of the techniques exercises are provided. The theoretical analysis is illustrated withthe empirical analysis of two sets of economic data. The theory has been developed in close contract with the application and the methods have been implemented in the computer package CATS in RATS asa result of a rcollaboation with Katarina Juselius and Henrik Hansen.