Estimation for nearly unit root processes with GARCH errors  

作　　者：YUAN Yu-ze ZHANG Rong-mao Department of Mathematics, Zhejiang University, Hangzhou 310027, China 

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第3期297-306,共10页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(10801118);Specialized Research Fund for the Doctor Program of Higher Education(200803351094)

摘　　要：In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.

关 键 词：Nearly unit root GARCH error least square estimation Ornstein-Uhlenbeck process empirical likelihood. 

分 类 号：O212.1[理学—概率论与数理统计]