Pitfalls in testing for long run relationships

This paper analyzes the robustness of the two most commonly used cointegration tests: the single equation based test of Engle and Granger (EG) and the system based test of Johansen. We show analytically and numerically several important situations where the Johansen LR tests tend to find spurious cointegration with probability approaching one asymptotically. The situations investigated are of two types. The first one corresponds to variables that have long-memory properties and a trending behavior, but they are not pure I(1) processes although they are difficult to tell from I(1) with standard unit root tests. The second corresponds to I(1) variables whose VAR representation has a singular or near-singular error covariance matrix. In most of the situations investigated in this paper, EG test is more robust than Johansen LR tests. This paper shows that a proper use of the LR test in applied cointegration analysis requires a deeper data analysis than the standard unit root test. We conclude by recommending to use both tests (EG and Johansen) to test for cointegration in order to avoid or to discover a pitfall.