长记忆ARFIMA-GARCH模型的状态空间模型估计

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.