This paper improves previous sufficient conditions for stationarity obtained in the context of a general nonlinear vector autoregressive model with nonlinear autoregressive conditional heteroskedasticity. The results are proved by using the stability theory developed for Markov chains....

This paper studies the stability of nonlinear autoregressive models with conditionality heteroskedastic errors. We consider a nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a nonlinear first order generalized autoregressive conditional heteroskedasticity...

This paper improves previous sufficient conditions for stationarity obtained in the context of a general nonlinear vector autoregressive model with nonlinear autoregressive conditional heteroskedasticity. The results are proved by using the stability theory developed for Markov chains....

This paper studies a class of Markov models which consist of two components. Typically, one of the components is observable and the other is unobservable or `hidden`. Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two...

This note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q...