Evaluating a class of nonlinear time series models

We consider a recently proposed class of nonlinear time series models and focus mainly on misspecification testing for models of such type. Following the modeling cycle for nonlinear time series models of specification, estimation and evaluation we first treat how to choose an adequate transition function and then contribute to the evaluation stage by proposing tests against serial correlation, no remaining nonlinearity and parameter constancy. We also consider evaluation by generalized impulse response functions. The finite sample properties of the proposed tests are studied via simulation. We illustrate the use of these methods by an application to real exchange rate data.