Geometric ergodicity of the ar processes perturbed by nonlinear random functions

Abstract

본 논문에서는 X_(n+1)=Φ_(n+1)(X_(n-(k-1)), …, X_(n-1), X_(n))+η_(n+1) 의 AR 모형에 대한 Ergodicity 와 Geometric Ergodicity의 충분조건을 찾고 그 조건을 이용해서 New Laplace Autoregressive Model of Order(p)와 ARCH Model 의 Geometric Ergodicity를 보인다.;We consider the kth -order auto regressive model which is given by X_(n+1) =Φ_(n+l)(X_(n-(k-1)), …, X_(n-1), X_(n)) +η_( n+l) (n ≥k - 1), where ｛Φ_(n)｝ is a sequence of i.i.d. random elements taking values on □, ｛η_(n)｝are i.i.d. random variables and ｛Φ_(n)｝ and ｛η_(n)｝ are independent each other. Here □ is a collection of Bore1 measurable function from R^(k) to R . We give sufficient conditions for the ergodicity and geometric ergodicity of the above model. By our results, we show that ARCH model and New Laplace Autoregressive Model of Order(p) are geometrically ergodic under some conditions.