Smooth transition autoregressive models are a flexible family of nonli
near time series models that have also been used for modelling economi
c data. This paper contributes to the evaluation stage of a proposed s
pecification, estimation, and evaluation cycle of these models by intr
oducing 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.