一种新的时间序列TC型异常值稳健检测法  

A New Robust Detection Method for TC-type Outliers in Time Series

作　　者：汪志红 王志坚 王斌会[3] Wang Zhihong;Wang Zhijian;Wang Binhui(School of Financial Mathematics&Statistics,Guangdong University of Finance,Guangzhou 510521,China;School of Statistics&Mathematics,Guangdong University of Finance&Economics,Guangzhou 510320,China;School of Management,Jinan University,Guangzhou 510632,China)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521 [2]广东财经大学统计与数学学院,广州510320 [3]暨南大学管理学院,广州510632

出　　处：《统计与决策》2023年第1期46-49,共4页Statistics & Decision

基　　金：国家社会科学基金资助项目(18BGL131)。

摘　　要：时间序列异常值检测是时间序列分析研究中的重要内容,然而,在实际检测中往往存在“遮蔽效应”问题。文章分析了已有研究提出的时间序列TC型异常值检测法的不稳健性,并从两个方面进行改进:第一,建立基于Huber权函数的稳健ARMA模型,得到无干扰AR系数与MA系数;第二,用绝对离差中位数作为残差稳健估计量。通过以上改进得到了TC型异常值稳健检测统计量,并通过模拟对比小样本、中样本、大样本,轻污染、中污染、重污染情形下传统检测法与稳健检测法的检测效力,结果发现:在小样本、轻污染率下,两种检测法相差不大,但随着样本量、污染率的增加,稳健检测法显著优于传统检测法。最后,稳健检测法的优良性在金融市场异常现象检测中得到进一步说明。Time series outlier detection is an important content in time series analysis.However,there is a problem of“shadowing effect”in actual detection.This paper analyzes the un-robustness of the time series TC-type outlier detection method proposed by the existing studies,and improves it from the following two points:First,a robust ARMA model based on the Huber weight function is established,and the undisturbed AR coefficient and MA coefficient are obtained.Second,the median absolute deviation is used as the robust estimator of residuals.Through above improvements,the robust detection statistic of TC-type outliers is obtained.Then,by simulating and comparing small sample,medium sample,and large sample,light pollution,medium pollution,and heavy pollution,the detection efficiency of traditional detection methods and robust detection methods is compared.The results show that there is little difference between the two detection methods in the case of small sample size and light pollution rate,but with the increase of sample size and pollution rate,robust detection method is significantly superior to traditional detection method.Finally,the merits of the robust detection method are further illustrated in the detection of anomalies in financial markets.

关 键 词：遮蔽效应 TC型异常值 异常值检测 稳健估计 

分 类 号：O212.1[理学—概率论与数理统计] F224[理学—数学]