Spurious Regression, Cointegration, and Near Cointegration : A Unifying Approach

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, a notion of near cointegration is proposed and three separate applications of the model of near cointegration are provided. As a first application, we give analytical corroboration of the conjecture that the finite sample behavior of F-statistics based on OLS estimators depends continuously on the aforementioned squared multiple correlation coefficient. Hence, the notion of near cointegration helps to bridge the gap between the polar cases of spurious regression and cointegration. Secondly, we characterize the properties of conventional cointegration methods under near cointegration, hereby investigating the robustness of cointegration methods. Finally, we illustrate how to obtain local power functions of cointegration tests that take cointegration as the null hypothesis