Abstract
We consider a general nonlinear ARMA( p, q) model X n+1 = h( e n− q+1 ,…, e n , X n− p+1 ,…, X n )+ e n+1 , where h : R p+q→R is a measurable function and {e n : n⩾1} is an i.i.d. sequence of random variables. Sufficient conditions for stationarity and geometric ergodicity of { X n } are obtained by considering the asymptotic behaviours of the associated Markov chain.
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