Geometric ergodicity of the non-linear AR-ARCH models

Abstract

본 논문에서는 다음과 같이 주어진 AR-processing (ARCH) 모형 에 대한 Geometric Ergodicity 의 충분조건을 찾고, Y_(t+i_(q+1))= g₁(Y(t+i₁),…, Y(t+i)) + g₂(Y(t+i₁),…, Y(t+i_q)) e(t+i_(q+1)) 또, 1995년 Tjstheim 와 Masry 의해 발표된 논문에 나온 충분조건의 의미를 생각하고, 그것이 항상 성립하지 않음을 보인다.;We consider the qth-order autoregressive conditional heteroskeda- stic(ARCH) model which is given by Y_(t+i_(q+1))= g₁(Y(t+i₁),…, Y(t+i)) + g₂(Y(t+i₁),…, Y(t+i_q)) e(t+i_(q+1)) where ｛e_t｝is an independent and identically distributed(i.i.d) sequence of random variables with means 0 and variance 1, and g₁and g₂are measurable functions on R^q. In this paper, we give a sufficient condition for geometric ergodicity of the above model by using Tweedie(1975,1988)-type criterion, and compare this result with the other condition which is given by TjΦstheim & Masry (1995) .