Time Series Change Point Detection And Application Based On Self-normalization Method

In recent years,change point detection has become a popular direction in statistics.It is widely used in fields such as medicine,engineering and finance.However,the existing change point detection methods are complex and diverse,but their effect is not ideal when detecting change points near sequence endpoints.Therefore,this paper investigates related methods to improve the ability to detect change points near endpoints and apply them to real datasets.First,this paper introduces the research progress of change point detection,and briefly introduces related methods such as local comparison method,CUSUM method and likelihood ratio method.This paper introduces the self-normalization method(SN)later and the reasons for its poor performance in detecting change points near endpoints,and focuses on the adaptive location self-normalization method(LASN)that can improve the ability to detect change points near endpoints.On the basis of theoretical introduction,this paper further designs simulation experiments,and this paper draws the following findings: First,no matter which method is used,the greater the difference before and after the change point,the easier it is to be recognized.Second,when the SN method is used in combination with the likelihood ratio test,it fails to improve the ability to detect change points near the endpoints,and it is almost impossible to detect the change points near the endpoints.Third,the highlighted LASN method outperforms traditional SN methods and likelihood ratio methods in detecting change points near endpoints.Finally,whether it is the LASN method,the SN method or the likelihood ratio method,there is a problem of reduced test power when detecting sequences with a high degree of auto correlation.Finally,this paper applies the LASN method,which can significantly improve the ability of change point detection near the endpoint,to the change point detection of the daily cumulative growth rate data of the Covid data of the United States,the United Kingdom and India.The change points in the data were found by the LASN method,and the reasons for the change points were explained.