Nonparametric Change Point Detection Under Piecewise Trend And Its Application Research

Many existing change point detection methods only focus on mutations such as mean or variance,while there are relatively few studies on trend gradual changes.Sudden changes are easy to find in actual data,but gradual changes are relatively difficult.In addition,there will be mixed situations with both gradual changes and mutations of variance.Therefore,this article mainly studies the piecewise linear trend change point and the variance change point of residual,and separately studies two adaptive change point detection methods,as follows.Aiming at the problem of gradual change points with linear trends,under the assumption that random noise is independent and obeys the same normal distribution,an efficient and ASBS(Adaptive Subinterval Binary Segmentation)method is studied.This method first adopts a fixed construction method for the detection sub-interval to make it adaptive;then uses the test statistics to detect the single change point of the data in the sub-interval,and combines the binary segmentation and expands it to multi-change point detection;Finally,the s SIC(strengthened Schwarz Information Criterion)method is used to obtain the trend change point,and the consistency of the ASBS method in detecting the number and location of the change point is proved.Numerical simulation analysis results show that compared with methods such as NOT(Narrowest-Over-Threshold)and ID(Isolate-Detec),The ASBS method detects the number of change points in piecewise linear trend data with higher accuracy,and the mean square error and Hausdorff distance are not much different from NOT and ID.Empirical analysis of traffic flow data in Shenzhen in 2018,the detection results are consistent with the morning,midnight and evening peak characteristics of traffic flow data,which shows the effectiveness of this method.In the residual variance change point research,the residuals are obtained by linear fitting the data according to the detection results of the ASBS method,and the adaptive estimation method WBS2-V(Wild Binary Segmentation 2 for Variance)of the residual variance change points is studied.Under given conditions,the position of the change point is estimated by maximizing the CUSUM(Cumulative Sum)of square statistic,and the consistency of the estimator is given;and adopt the idea of random positioning,combined with binary segmentation and s SIC to obtain an estimate of variable points.Simulation studies have shown that the Hausdorff distance of this method decreases with the increase of the sample size,and the mean square error decreases as the sample size increases,indicating that the algorithm is consistent.Applying the ASBS method and this method to OPEC oil price data in turn,the results show that most of the detected change points have corresponding international events,indicating that this method has strong practical value.The two adaptive methods studied in the article have achieved good results under certain conditions and under the influence of different errors.The segmented trend change point reflects the process of data from quantitative change to qualitative change or quantitative change caused by qualitative change,while the variance change point reflects the abnormal sudden change of data in fluctuations.The combination of the two methods can detect mixed changes.In consequence,the scope of application of the research content of this article is wide,and it has certain practical significance.