一类带有GARCH类误差项的自回归滑动平均模型

doi:10.16088/j.issn.1001-6600.2021083003

广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (1): 195-205.doi: 10.16088/j.issn.1001-6600.2021083003

一类带有GARCH类误差项的自回归滑动平均模型

梁鑫^1*, 陈小玲¹, 张兴发^1,2, 李元^1,2

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

收稿日期:2021-08-30 修回日期:2021-09-15 出版日期:2022-01-25 发布日期:2022-01-24
通讯作者: 梁鑫(1978—), 男, 广西梧州人, 广州大学博士研究生。E-mail: liangxin@gxnu.edu.cn
基金资助:
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)

A Class of Autoregressive Moving Average Model with GARCH Type Errors

LIANG Xin^1*, CHEN Xiaoling¹, ZHANG Xingfa^1,2, LI Yuan^1,2

1. School of Economics and Statistics, Guangzhou University, Guangzhou Guangdong 510006, China;
2. Lingnan Research Institute of Statistical Science, Guangzhou University, Guangzhou Guangdong 510006, China

Received:2021-08-30 Revised:2021-09-15 Online:2022-01-25 Published:2022-01-24

摘要/Abstract

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。

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

Abstract: 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.

Key words: autoregressive moving average model, DAR model, quasi-maximum likelihood estimation, moment condition, asymptotic normality

中图分类号:

O212.1

梁鑫, 陈小玲, 张兴发, 李元. 一类带有GARCH类误差项的自回归滑动平均模型[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 195-205.

LIANG Xin, CHEN Xiaoling, ZHANG Xingfa, LI Yuan. A Class of Autoregressive Moving Average Model with GARCH Type Errors[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 195-205.

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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

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