Consistent Model Specification Tests Against Smooth Transition Alternatives

In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition" models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), provides maximal power against nonlinear smooth transition ARX specifications, and is consistent against any deviation from the null hypothesis. Of separate interest, we provide substantial detail regarding when and whether Bierens-type tests are asymptotically degenerate. In a simulation experiment in which all parameters are randomly selected, and a linear AR null model is selected by minimizing the AIC, the proposed test has power nearly identical to a most powerful test for true STAR processes, and dominates popular tests.