Nonlinear time series models and weakly dependent innovations

This paper provides a strict stationarity proof for general nonlinear regression models. In particular, it shows the existence of a strictly stationary solution to first order dynamic nonlinear models when the innovations are only assumed to satisfy a strict stationarity or strong mixing condition. The results of this paper can be applied to show the strict stationarity of threshold unit root models under general conditions that include weak dependence assumptions on the innovations. Previous results of this type were derived using a Markov chain approach, which uses an i.i.d. assumption on the innovations. The results are applied to threshold autoregressive models to yield strict stationarity results for threshold unit root models in the presence of weakly dependent errors.