Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes

In this paper we attempt to establish unified sufficient conditions for geometric ergodicity of autoregressive models. It is shown that there is a close relationship between geometric ergodicity and mixing properties. The case of nonstationary time series is incorporated into the investigations. Several time series models including threshold and EXPARCH-models are examined with respect to geometric ergodicity. In some cases we obtain regions of geometric ergodicity in the parameter space, which are larger than that known from the literature. Copyright 2005 Blackwell Publishing Ltd.