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

This paper introduces a representation of an integrated vectortime series in which the coefficient of multiple correlation computed fromthe long-run covariance matrix of the innovation sequences is a primitiveparameter of the model. Based on this representation, a notion of nearcointegration is proposed and three separate applications of the model ofnear cointegration are provided. As a first application, we give analyticalcorroboration of the conjecture that the finite sample behavior ofF-statistics based on OLS estimators depends continuously on theaforementioned squared multiple correlation coefficient. Hence, the notionof near cointegration helps to bridge the gap between the polar cases ofspurious regression and cointegration. Secondly, we characterize theproperties of conventional cointegration methods under near cointegration,hereby investigating the robustness of cointegration methods. Finally, weillustrate how to obtain local power functions of cointegration tests thattake cointegration as the null hypothesis.