Geometric Ergodicity for Asymmetric Power GARCH(p,q) Model

Abstract

Engle(1982)과 Bollerslev(1986)에 의해 ARCH/GARCH 모형이 소개되었으며, 특히 GARCH 모형은 재무 자료의 변동성과 heavy tail을 설명하는 데에 널리 이용되어 왔다. 또한, GARCH 모형의 여러 변형된 형태가 소개되었는데, 이 논문에서는 그 중에서도 Ding, Anderson, Engle(1993)에 의해 제안된 asymmetric power GARCH 모형을 다루었다. APGARCH 모형의 stationarity와 geometric ergodicity 를 위한 조건을 제시하고, 이를 보이기 위해서 drift condition과 Tweedie(2001)의 정리를 이용하였다.;The autoregressive conditional heteroscedastic model (ARCH) and the classical generalized autoregressive conditional heteroscedastic model (GARCH) were introduced by Engle(1982) and Bollerslev(1986). The GARCH model explains the time varying volatility and heavy tail property, and many extension of classical GARCH model have been developed. In this paper, we consider the augmented asymmetric power GARCH model which was introduced by Ding, Anderson and Engle(1993). We give the condition for stationarity and the geometric ergodicity. The geometric ergodicity is derived from the drift condition and Theorem 2.3 (Tweedie (2001)), by using connection between irreducibility and the existence of a unique invariant measure under the uniform countable additivity condition.