On geometric ergodicity of CHARME models


Correspondence to: Jean-Pierre Stockis, Department of Mathematics, University of Kaiserslautern, Erwin-Schroedinger-Str., 67663 Kaiserslautern, Germany.

E-mail: stockis@mathematik.uni-kl.de


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 derive asymptotic stability of this model. These results form the basis for deriving an asymptotic theory for nonparametric estimation. As an illustration, neural network sieve estimates for the autoregressive and volatility functions are considered, and consistency of the parameter estimates is obtained.