Testing for cointegration in nonlinear smooth transition error correction models

This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.