Geometric ergodicity of nonlinear autoregressive models with changing conditional variances

Abstract

Abstract The authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random processxt= ϕ(xt‐1,…,xt‐p) + ϵtσ(xt‐1,…,xt‐q) in which ϕ: Rp→ R, σ Rq→ R and (ϵt) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.

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