Testing the adequacy of smooth transition autoregressive models

Smooth transition autoregressive models are a flexible family of nonlinear time series models that have also been used for modelling economic data. This paper contributes to the evaluation stage of a proposed specification, estimation, and evaluation cycle of these models by introducing a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM-type tests for the hypothesis of no remaining nonlinearity and that of parameter constancy. Small-sample properties of the F versions of these tests and some alternative test statistics are investigated by simulation. The results indicate that the proposed tests can be applied in small samples already.