Abstract
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 this models by introducing a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM type tests for the hypothesis of remaining nonlinearity and that of parameter constancy. Small sample properties of the F versions of the tests and some alternative tests are investigated by simulation. The results indicate that the proposed tests can be applied in small samples already.