Nonparametric Change Point Estimation Based On MOSUM

In the current research of change point problem,when the data changes greatly in a short period of time and changes little in a long period of time,the existing detection methods will have the situation of false detection or missing detection,and the calculation cost is relatively large.In view of this,this paper aims to study an efficient mean change point detection method based on MOSUM(Moving Sum)statistics,the statistical properties,detection efficiency and parameter robustness of this method will be studied as follows.In this paper,we study the statistical properties of change point estimators for MOSUM statistics.In the classical mean change point model,we extend the detection results with multiple deterministic changes by considering the random changes in the hidden Markov regime switching models.In view of this,firstly,we consider the multiple mean change point model with possible time series errors,and the number and position of the change points can be estimated uniformly by this method.In addition,the convergence rate of change point position is strict.Secondly,because the estimation performance of the sample depends on the estimation of the asymptotically long-run variance of the error sequence,it is proposed to use the MOSUM estimator to estimate the square error,and its asymptotic properties are derived,Considering the influence of the window width on the test statistics,this paper proposes the combined width of MOSUM test(MMT).Simulation results show that the proposed method has better performance in small sample estimation than the existing methods.Based on the research of MMT method,in order to make the method more universal and practical,a multiple filter test(MFT)method is further constructed.The research shows that MFT method has three important advantages.First,the model can make a general distribution assumption,that is,it can assume 4).4).(9.random segmented sequence changes,but also relax the identical distribution or independence.Second,this method uses MOSUM statistics and asymptotic settings to make the MOSUM process weakly converge to the function of Brownian motion,and is further used to simulate the rejection threshold of statistical test.At the same time,MFT can apply multiple MOSUM processes at the same time,so as to improve the detection of change points in different time ranges.Finally,the simulation results show that MFT method has more advantages in detection accuracy and accuracy than other existing methods.Aiming at the practicability of the method,the paper analyzes the traffic data and stock data,and the results show that the two methods can identify the change points in the data,obtain their internal laws,provide some guidance for the relevant departments,and have certain practical significance.