一类带有GARCH类误差项的自回归滑动平均模型  

A Class of Autoregressive Moving Average Model with GARCH Type Errors

作　　者：梁鑫 陈小玲 张兴发 李元[1,2] LIANG Xin;CHEN Xiaoling;ZHANG Xingfa;LI Yuan(School of Economics and Statistics,Guangzhou University,Guangzhou Guangdong 510006,China;Lingnan Research Institute of Statistical Science,Guangzhou University,Guangzhou Guangdong 510006,China)

机构地区：[1]广州大学经济与统计学院,广东广州510006 [2]广州大学岭南统计科学研究院,广东广州510006

出　　处：《广西师范大学学报（自然科学版）》2022年第1期195-205,共11页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11731015,11701116);广东省普通高校创新团队项目(2020WCXTD018);广州大学科研基金(YG2020029,220030401)。

摘　　要：本文结合DAR模型及传统的ARMA-GARCH模型,提出一类带有新型GARCH类误差项的自回归滑动平均模型。该模型比DAR模型引入更多数据信息,同时定义一种由可观测序列驱动的新型条件异方差结构,比传统ARMA-GARCH模型的条件方差更易于估计。本文研究模型参数的拟极大似然估计,并在较弱矩条件下证明估计量的渐近正态性;数值模拟结果证实该模型在有限样本下的有效表现;实证研究表明:该模型可以提高数据拟合效果,因而具有一定应用价值。In this paper,an autoregressive moving average model with a new GARCH error term is proposed by combining DAR model and traditional ARMA-GARCH model.This model introduces more data information than the DAR model,and defines a new conditional heteroscedasticity structure driven by observable sequence,which is easier to estimate than the traditional ARMA-GARCH model.The article studies the quasi-maximum likelihood estimation of the model parameters,and proves the asymptotic normality of the estimator under weaker moment conditions.Numerical simulation results confirm the effective performance of the model under finite samples.Empirical research shows that this model can improve the data fitting effect,and has certain value of applications.

关 键 词：自回归滑动平均模型 DAR模型 拟极大似然估计 矩条件 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]