Ergodicity, geometric ergodicity and mixing conditions for nonparametric ARMA processes

Abstract.

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 themoving average structure depend only one step behind. Also, a Fisher-consistent procedure is provided and its performance is studied through a simulated example.