Abstract: We identify conditions for geometric ergodicity of general, and possibly nonparametric, nonlinear autoregressive time series. We also indicate how a condition for ergodicity, with minimal side assumptions, may in fact imply geometric ergodicity. Our examples include models for which exponential stability of the associated (noiseless) dynamical system is not sufficient or not necessary, or both.
Key words and phrases: Ergodicity, Markov chain, nonlinear time series.