Detecting equilibrium correction with smoothly time-varying strength

Simulations are used to check the probability of detecting a time-varying equilibrium correction by applying the existing tests of no cointegration and parameter constancy. Smooth transition regressions are chosen to describe the nonlinearity and the Johansen cointegration test and the Lin and Teräsvirta parameter constancy test are applied. It turns out that both tests perform well separately but the joint power is quite low. The most notable result of this study is the high power when dealing with unrestricted cointegration, that is, when no cointegrating vector is estimated and the cointegrated variables freely enter the model in levels. The power of the parameter constancy test for the unrestricted cointegration is close to the power when the cointegrating vector is assumed to be known.