基于稳健Cook距离的时间序列异常值诊断

Outlier Diagnosis of Time Series Based on Robust Cook Distance

Cook距离公式常用于回归模型的异常值诊断,但由于公式中的样本方差■对异常值敏感,导致公式缺乏稳健性,使得诊断效果不理想。基于以上问题,文章选取绝对离差中位数作为样本标准差的稳健估计量,得到了样本方差■的稳健估计量,进而构造出稳健Cook距离公式;借鉴传统Cook距离的回归模型异常值诊断理论,将稳健Cook距离公式应用于时间序列异常值诊断,拓展了传统Cook距离公式的异常值诊断领域。通过选取模拟样本量分别为50、100、200,污染率分别为0、1%、5%、10%的ARMA(1,1)序列及金融时间序列进行实例分析,结果发现:(1)在无污染时,稳健Cook距离法与常规Cook距离法的诊断正确率均为100%,两者没有出现"误诊"现象;(2)在样本量、污染率同时增大时,常规Cook距离诊断正确率急剧下降,当污染率达到5%及以上时,已基本无诊断力,而稳健Cook距离法依然能保持较高的诊断力。稳健Cook距离法不仅能应用于时间序列异常值诊断,也能应用于回归分析的异常值诊断。

Cook distance formula is often used in outlier diagnosis of regression models,but the sample variance ■ in the formula is sensitive to outliers,resulting in the lack of robustness of the formula,which makes the diagnosis effect unsatisfactory.In view of the above problem,this paper selects the median absolute deviation as the robust estimator of sample standard deviation to obtain the robust estimator of sample variance ■,and further construct the robust Cook distance formula,and then based on the outlier diagnosis theory of regression model of traditional Cook distance,applies the robust Cook distance formula to outlier diagnosis of time series,expanding the field of outlier diagnosis of traditional Cook distance formula.Finally,the paper conducts case analyses by selecting ARMA(1,1) series and financial time series with simulated sample sizes of 50,100 and 200 and pollution rates of 0,1%,5%and 10%.The results are shown as follows:(1) When there is no pollution,the diagnostic accuracy of robust Cook distance method and conventional Cook distance method are 100%,with no“misdiagnosis”;(2) When the sample size and pollution rate increase at the same time,the diagnostic accuracy of conventional Cook distance decreases sharply;when the pollution rate reaches 5%and above,it has basically no diagnostic power,while the robust Cook distance method can still maintain high diagnostic power.The robust Cook distance method can not only diagnose outliers of time series,but also be applied to the outlier diagnosis of regression analysis.