关于随机差分方程的一个注记及其在GARCH模型中的应用(英文)  

A Note on Stochastic Difference Equations and its Application to GARCH Models

作　　者：张志强[1] 汤家豪[2] 

机构地区：[1]华东师范大学统计系,上海200062 [2]香港大学统计与精算学系

出　　处：《应用概率统计》2004年第3期259-269,共11页Chinese Journal of Applied Probability and Statistics

基　　金：This projecl was partly supported by the National Social Science Foundation of China(No.03BTJ006).

摘　　要：本文对Kesten(1973)中的关于随机矩阵的更新理论作了一个注记,给出了一个计算尾部指数k1的一个简易方法,并利用此讨论了ARCH(2)和GARCH(2,1)两个时间序列模型的平稳域和分布尾部概率,同时给出了一些直观的数值结果.本文结果可看作是对Embrechts et al.(1997)和Mikosch及Starica(2000)关于一维随机差分方程应用结果的一个推广.In this paper, we give a note to the renewal theory for products of random matrices in Kesten (1973), and give a feasible way to calculate the tail exponent k1 in the renewal theory. As an application, the stationarity and the tail behaviour of ARCH(2) and GARCH(2,1) time series models are studied. Our work is a generalization of similar work on ARCH(1) by Embrechts et al. (1997) and on GARCH(1,1) by Mikosch and Starica (2000). Some numerical results are also given in this paper.

关 键 词：随机差分方程 更新理论 ARCH GARCH 尾部状态 尾部指数 LYAPUNOV指数 

分 类 号：O211.61[理学—概率论与数理统计] O211.3[理学—数学]