稳健AR模型的构建及比较研究  

The Formation and Comparison of Robust AR Model

作　　者：王志坚 王斌会[2] WANG Zhi-jian;WANG Bin-hui(School of Statistics & Mathematics,BigData and Educational Statistics Applied Laboratory GuangdongUniversity of Finance & Economics,Guangzhou 510320,China;School of Management,Jinan University,Guangzhou 510632,China)

机构地区：[1]广东财经大学统计与数学学院大数据与教育统计应用实验室,广东广州510320 [2]暨南大学管理学院,广东广州510632

出　　处：《数学的实践与认识》2019年第13期156-166,共11页Mathematics in Practice and Theory

基　　金：国家社科基金一般项目:稳健统计过程控制的大数据分析方法研究(16BTJ035);广东省自然科学基金项目:稳健过程控制图的构建及评价方法研究(2016A030313108);中国博士后科学基金第62批面上资助项目《时序数据的稳健统计过程控制方法研究及其应用》(2017M622718)

摘　　要：时间序列自回归AR模型在建模过程中易受离群值的影响,导致计算结果与实际不相符.针对这一现象,将Hampel权函数运用于自相关函数中,从而构建出自回归AR模型的稳健估计算法,以克服离群值的影响.并对此方法进行了模拟和实证分析,模拟和实证分析均表明:当时序数据中不存在离群值时,传统估计方法与稳健估计方法得到的结果基本保持一致;当数据中存在离群值时,运用传统估计方法得到的结果出现较大变化,而运用稳健估计方法得到的结果基本不变.这说明相对于传统估计方法,稳健估计方法能有效抵抗离群值的影响,具有良好的抗干扰性和高抗差性.The AR model of time series were easily be interfered by outliers when model ing,which will lead to the outcome of modeling deviates from the fact.In reaction to the phenomenon,in this paper the Hampel Weight Function is applied to the autocoirelation function,and then the robust algorithm of AR model was formation to avoid the disturbance from outliers,also we made the digital simulation and the empirical analysis on the basis of robust algorithm of aut ocoirelation function We found that the results of the traditional estimate method and the robust estimate method were basically the same when there were no outliers in the data;the results from the traditional estimate method changed considerably while robust,estimate method remained consistent when there were outliers in the data.This comparison showed that the robust estimate method,which had good anti-interference and high reliability,could efficiently avoid the disturbance from the outliers.

关 键 词：AR模型 稳健统计量 稳健估计 离群值 

分 类 号：O212.1[理学—概率论与数理统计] F832.51[理学—数学]