稳健残差控制图的构建及在金融时序中的应用  

The Construction of Robust Residual Control Chart and Its Application in Financial Time Series

作　　者：王志坚[1] 

机构地区：[1]广东财经大学统计与数学学院,广东广州510032

出　　处：《数理统计与管理》2017年第5期930-942,共13页Journal of Applied Statistics and Management

基　　金：国家社科基金一般项目(16BTJ035);广东省自然科学基金项目(2016A030313108)资助

摘　　要：对于呈现自相关和波动族聚性并存的受控过程,通常采用残差控制图对其进行监控。但异常点的存在会对自相关或波动族聚性模型的拟合产生重要影响,使得基于该模型的残差并非独立同分布导致常规残差控制图监控失效。为解决这类问题,本文提出稳健残差控制图。即建立稳健的ARMA模型解决自相关问题从而得到无自相关的残差序列,用稳健的GARCH模型来构建控制图的上下限。模拟和实证研究表明,本文提出的稳健残差控制图具有很好的抗异常点能力并能更好的对金融时间序列的异常现象进行监控。When there is a process which appears autocorrelation and volatility clustering, we usually adopts the Residual Control Chart to monitor it. But the presence of outliers in data may extremely affect the autocorrelation and volatility clustering model fitted. Which will result to the residual based on the model weren＇t independent and identically distributed, so the conventional Residual Control Chart fail to monitor the process. To solve this problem, this paper puts forward a Robust Residual Control Chart. That is construct a robust ARMA model for autocorrelation, then we get non-autocorrelation residual series; on the other hand, the upper and lower limits of control chart were constructed by robust GARCH model. Simulation and empirical study show that the Robust Residual Control Chart which proposed by this article could resist to outliers effectively, and also can monitor the abnormal phenomenon in financial time series betterly.

关 键 词：统计过程控制 稳健残差控制图 金融时间序列 异常点检测 

分 类 号：O212[理学—概率论与数理统计]