Linearity and misspecification tests for vector smooth transition regression models

In this paper, we derive Lagrange multiplier and Lagrange multiplier type specification and misspecification tests for vector smooth transition models. We report results from simulation studies in which the size and power properties of the proposed tests in small samples are considered. The results show that these asymptotic tests generally suffer from size distortion. We find that Wilks’s and Rao’s F statistic both have satisfactory size properties and can be recommended for empirical use. Bootstrapping the standard asymptotic LM statistic offers another solution to the problem.