Ergodicity, geometric ergodicity and mixing conditions for nonparametric ARMA processes

In this paper, we introduce nonparametric ARMA models which provide an alternative to nonparametric autoregressive models, when there is a large dependence to the past observations. Conditions for ergodicity and geometric ergodicity are given when both the nonparametric autoregressive part and the moving average structure depend only one step behind. Also, a Fisher-consistent procedure is provided and its performance is studied through a simulated example.