COMPARISON OF SOME NON‐LINEAR AUTOREGRESSIVE PROCESSES

Göran Högnäs

Journal of Time Series Analysis, 1986, vol. 7, issue 3, 205-211

Abstract: Abstract. We investigate autoregressive processes {Xn} ({Y“}) satisfying Xn+1=Λ(Xn) + Zn+1(Yn+1=μ(Yn) + Zn+1), n = 0, 1, 2, …, where Λ and μ are odd increasing functions and the Zn‘s are i.i.d. with unimodal symmetric distribution. The process {|Xn|} is then stochastically monotone on [0, ∞). If |Λ| ≤ |μ| then |Xn is stochastically dominated by |Yn| for n = 1, 2, …. Some related asymptotic properties, e.g., stationary distributions, are also discussed.

Date: 1986
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