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On the Stationarity of First-order Nonlinear Time Series Models: Some Developments

In the present paper we consider the general class of first-order nonlinear models. The main contributions concern primerly a generalization of the conditions for geometric ergodicity presented in Ferrante et al. (2003). The obtained result is then applied to two classes of first-order nonlinear models not previously addressed. Secondly we apply to general firstorder nonlinear models some recently developed conditions for the existence of the invariant measure of a Markov process. For this class of nonlinear models we also prove that the usual drift-condition for geometric ergodicity for Markov chains still holds even in the presence of an alternative assumption than T-continuity.