Change Point Detection For Multivariate Time Series And Its Application Research

With the advent of the big data era,the technology of data analysis is particularly important and the change point problem is an important research branch in the data processing.Since 1970 s,more and more statisticians have paid attention to it.However,there are relatively few research results of change point detection for multivariate time series in the existing literatures.In this thesis,we mainly discuss change point detection of multivariate time series and its application in traffic flow data.Firstly,we decompose the unary time series by Local Stationary Wavelet(LSW)model,the wavelet periodogram is calculated,and then the Cumulative Sum(CUSUM)statistics are constructed.Estimating the number and location of the change points in the covariance structure for the univariate time series by Wild Binary Segmentation(WBS)method,simultaneously.And its consistency estimation are given.In addition,the validity of the WBS method is proved by the numerical simulation test.Compared with the Binary Segmentation(BS)and Likelihood Ratio Scan(LRS)methods,simulation results show that the calculation rate of WBS method is faster than the others and is also effective in the smaller jumps.Secondly,we decompose the multivariate time series by Multivariate Local Stationary Wavelet(MLSW)model,the wavelet periodograms and the cross wavelet periodograms are calculated,and then the CUSUM statistics are constructed by wavelet periodograms and the cross wavelet periodograms.The number and position of the change points in the two order structure for the multivariate time series or even high dimension time series are estimated by Sparse Binary Segmentation(SBS)method,simultaneously.And then the consistency proof are given.In addition,the simulation test results show that the effectiveness of the SBS method.By compared with average and maximum algorithms,threshold algorithm also has better test performance.Finally,the WBS method and SBS method are applied to the traffic flow data for univariate and multivariate in Guiyang for empirical analysis,respectively.The results show that the change points in traffic flow often appear during the rush hour,and can provide more accurate traffic congestion time for the traveler and the traffic management department,which also has practical significance to the traffic control.