Testing for nontrivial cointegration

Cointegration is pivotal in analyzing long-run equilibrium relationships among economic variables. Traditional cointegration models have been effective in handling mixed-order integrated variables, but they can lead to misleading conclusions from an equilibrium perspective if trend stationary observables are involved. This type of variable leads to the so-called trivial cointegration, which might falsely suggest a long-run relationship where none exists. Testing for nontrivial cointegration is possible using standard methods, but this necessarily requires a sequential approach, and it typically leads to an inconsistent test. This paper proposes a direct and consistent test for nontrivial cointegration in a bivariate setting motivated by the different behavior of the sample correlation between the observables under various cointegration scenarios. Our testing approach is compared with standard methods by means of a Monte Carlo experiment, and we include the analysis of an empirical application to the term structure of government nominal bond yields for the European Monetary Union area.