一类带有线性GARCH类误差的滑动平均模型  

A Class of Moving Average Model with Linear GARCH Type Errors

作　　者：陈小玲 张兴发 李元[1,2] 宋泽芳 CHEN Xiaoling;ZHANG Xing-fa;LI Yuan;SONG Ze-fang(School of Economics ajid Statistics,Guangzhou University,Guangzhou 510006,China;Lingnan Research Institute of Statistical Science,Guangzhou University,Guangzhou 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：《数学的实践与认识》2021年第18期118-131,共14页Mathematics in Practice and Theory

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：提出了一类带有线性GARCH类误差项的滑动平均模型,记作MA-LGARCH模型.该模型可以看成是p阶线性双自回归,即LDAR(p)模型,在p=∞情形下的一类推广.因而MA-LGARCH模型可以引入更多的数据信息,有助于数据分析结果的改进.文章运用拟极大似然估计方法对模型参数进行了估计,并在较弱矩条件下证明了估计量的渐近正态性.数值模拟结果显示估计量在有限样本下表现良好.基于国内外数据的实证研究表明,MA-LGARCH模型可以提高数据的拟合效果,因而有潜在的应用价值.This paper proposes a class of moving average models with linear GARCH type errors,denoted as MA-LGARCH model.This model can be regarded as an existing p-order linear double-autoregressive LDAR(p) model in the case of p=∞.Therefore,MA-LGARCH model can introduce more data information,which is helpful to improve the results of data analysis.In this paper,the parameters of the model are estimated by using the quasi maximum likelihood estimation method,and the asymptotic normality of the estimator is proved under the condition of weak moment.The numerical simulation results show that the estimator performs well under limited samples.The empirical studies based on domestic and foreign data show that the MA-LGARCH model can improve the fitting effect of the data,so it has potential application value.

关 键 词：滑动平均模型 LDAR模型 线性GARCH模型 

分 类 号：O212.1[理学—概率论与数理统计]