长记忆ARFIMA-GARCH模型的状态空间模型估计(英文)  

State Space Estimation for Long Memory ARFIMA-GARCH Models

作　　者：王立洪[1] 顾承祖[1] 

机构地区：[1]南京大学数学系,南京210093

出　　处：《应用概率统计》2011年第6期642-656,共15页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(11171147);the Natural Science Foundation of Jiangsu Province of China(BK2009222);by the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(708044)

摘　　要：本文考虑了ARFIMA-GARCH类模型的状态空间表示.ARFIMA-GARCH这类模型结合了长记忆时间序列和条件异方差过程.虽然ARFIMA-GARCH模型的状态空间表示是无穷维的,但是基于这种表示法的精确极大似然估计可以在样本长度的迭代计算中得到.本文提出了基于模型的截断的自回归展开式的似然函数近似估计,进而得到了模型参数的拟似然估计.利用状态空间表示的便利,本文的估计方法被应用到了缺失数据的情形.最后,我们还将本文的方法应用于模拟计算(缺失数据和非缺失数据)和实际数据分析.This paper considers the state space representation for the ARFIMA-GARCH model, which combines both the long memory time series and the conditional heteroscedastic processes. Although this state space representation is infinite dimensional, an exact maximum likelihood （ML） estimator based on this kind of representation can be computed in a finite number of iterations. Quasi ML estimators based on the autoregressive approximation for the likelihood function are proposed. Due to the facility of the state space representation, these estimation approaches can be easily applied to the missing data case. Simulation results of both the non-missing data case and the missing data case are reported. A real data example from stock market illustrates the proposed method.

关 键 词：ARFIMA-GARCH模型 极大似然估计 缺失数据 状态空间表示 

分 类 号：O211.61[理学—概率论与数理统计]