This paper introduces a representation of an integrated vector time series in which the coefficient of multiple correlation computed from the long-run covariance matrix of the innovation sequences is a primitive parameter of the model. Based on this representation, we propose a notion of near cointegration, which helps bridging the gap between the polar cases of spurious regression and cointegration. Two applications of the model of near cointegration are provided. As a first application, the properties of conventional cointegration methods under near cointegration are characterized, hereby investigating the robustness of cointegration methods. Secondly, we illustrate how to obtain local power functions of cointegration tests that take cointegration as the null hypothesis.