Research On Multiple Change-points Detection Algorithm Based On Peak Recognition

Change-point detection is an important research field in statistics.In recent years,the algorithms of change-point detection have emerged from a diverse range of areas,such as biomedicine,finance,and power science.This thesis mainly considers the problem of multiple change-points detection for mean change of independent time series data,and proposes some change-point detection methods based on the peak recognition algorithm from the perspectives of parameter estimation and hypothesis testing.The LASSO-type change-point algorithm is one of the most popular algorithms to solve the problem of multiple change-point detection from the perspective of parameter estimation in recent years.It transforms the traditional change-point detection problem into the variable selection problem of parameter estimation by introducing the lower triangular design matrix,so as to carry out the change-point detection.Using LASSO to solve the change-point problem not only can estimate the location and number of the change-point at the same time,but also has high computational efficiency.However,the LASSO-type change-point detection method also has some problems that cannot be ignored in practical applications.First,with the increase in data size,the lower triangular matrix introduced by the LASSO algorithm will increase with it,which will reduce the calculation speed;Secondly,the LASSO-type method only determines the position of the change-point by the value of the first-order difference between the mean of two adjacent points,which is not only easily affected by outliers,and the stability of the algorithm is tested,but also ignores the time series orderly characteristics of the data itself,and the distance between two adjacent change-points is difficult to control.In order to improve the above shortcomings,based on the original LASSO algorithm,this paper proposes a segmented multiple-LASSO and peak recognition algorithm.This algorithm is aimed at the change-point detection problem of longer time series data.By screening the original data,the efficiency of the LASSO-type change-point detection algorithm is improved.By using multiple differences,the local information of the data is fully utilized to enhance the stability of the algorithm.By introducing the idea of peak recognition,the timing of the data is taken into account,which better controls the distance between adjacent change-points.Since most of the change-point detection algorithms proposed from the perspective of parameter estimation have high computational complexity,this paper also provides two new change-point detection algorithms from the perspective of hypothesis testing,combined with the peak recognition algorithm.Generally,most of the change-point detection algorithms proposed from the perspective of hypothesis testing use the CUSUM test statistics.But,the detection result of the CUSUM statistics will be affected by the data distribution,that is,when the data are normal distribution,the statistics performs well.In practice,the normal distribution for the data is too harsh to obey.Therefore,from the idea of shape recognition,this thesis proposes a new test statistics ASCC to replace the traditional CUSUM statistics.The new statistics not only has no requirement for data distribution,which broadens the data types for algorithm applications,but also can fully describe the surrounding shape information of the detected position with a strong anti-interference ability.Based on ASCC statistics and longer time series data,this thesis proposes two algorithms,namely ASCC-SSPR and SMSA.Considering that the actual number of change-points is limited,in order to improve the efficiency of these algorithms,the ASCC-SSPR algorithm evenly divides the entire data sequence into some segments,selects segments that may contain change-points by testing,and performs change-point detection in these selected segments.The SMSA algorithm studies the characteristics of the density function of the original data statistics and introduces the sudden drop point.It screen out the most likely part of the change-point by the data itself and then performs change-point detection in these selected segments.SMSA algorithm draws on the idea of binary segmentation,and proposes a multiple segmentation idea,which further improves the speed of change-point detection.Both of these two algorithms use the peak recognition idea,which not only makes full use of the timing characteristics of the data,but also improves the robustness of these two algorithms.In summary,when studying the problem of multiple change-points detection for mean change of independent time series data,three change-point detection algorithms are proposed combined with the peak recognition algorithm,from the perspective of parameter estimation and hypothesis testing.This thesis not only verifies the effectiveness of these three algorithms and their certain advantages compared with some other algorithms through theoretical proofs and experimental studies,but also applies these three algorithms to actual data in the fields of biomedicine,electric power,and finance.Through actual cases,the rationality,practicability and economic value of these new algorithms proposed in this work are further verified.