On probabilistic properties of nonlinear ARMA(p,q) models

Abstract

We consider a general nonlinear ARMA(p,q) model Xn+1=h(en-q+1,...,en,X n-p+1,...,Xn)+en+1, where h:Rp+q→R is a measurable function and {en:n≥1} is an i.i.d. sequence of random variables. Sufficient conditions for stationarity and geometric ergodicity of {Xn} are obtained by considering the asymptotic behaviours of the associated Markov chain. © 2000 Elsevier Science B.V.