We consider a generalized mixture of nonlinear AR models, a hidden Markov model for which the autoregressive functions are single layer feedforward neural networks. The nontrivial problem of identifiability, which is usually postulated for hidden Markov models, is addressed here.

In this article we consider a CHARME model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. To provide sets of conditions under which such processes are geometrically ergodic and, therefore, satisfy some mixing conditions, we apply the theory of Markov chains to...