Here, we extend the concept of cointegration from single-equation analysis to systems containing unit root data. We begin with a discussion of the intuition of vector cointegration and introduce the VECM, which is the basis for estimation of cointegrated VARs. We discuss the method for estimation of the VECM. In parallel to Chapter 8, we describe how to build the model that will be used to test for cointegration. We then introduce tests for the existence of multiple cointegrating relationships. If there are one or more cointegrating relationships, the model is reestimated imposing that number of cointegrating relationships. This model is referred to as the unrestricted reduced rank model. We discuss the identification problems inherent in the unrestricted reduced rank model, as well as what can be learned from this model. Next, we present a number of hypothesis tests that can be conducted to aid in identifying reasonable restrictions to impose on the model and explain how to impose restrictions in practice. We cover two different interpretation strategies as well and then offer a practical guide to cointegrated vector autoregression and an application.