Study On The Change Points Of Time Series Baesed On Bayesian Method

Change point statistical analysis has always been a key research topic in the field of mathematical statistics.The initial research on change points was proposed from industrial quality control.Up to now,change point theory has been involved in many fields,such as hydrological statistics,earthquake prediction,traffic data processing,and financial measurement.In recent years,more and more statisticians have chosen Bayesian statistical methods to study the method of changing points.This paper is interested in how to use Bayesian method to detect the change points in time series models.On the basis of familiarity with the relevant theoretical knowledge of change points,this paper first discusses several commonly used change point detection methods,and points out the applicable situations of these methods.The next step is to use the Bayesian theory method to discuss the AR model.Change point problem.Due to the complexity of the change point problem,this paper starts with the first-order autoregressive model,and derives the display expression of Bayesian estimation of single change point in AR(1)model by theoretical derivation,and then generalizes it to On the change point of the high-order AR model,according to the results of the displayed expressions,the Matlab language program is written to perform the corresponding numerical simulation to verify the validity of the Bayesian method for detecting the change points.Finally,in order to reduce the iteration In this paper,the Gibbs sampling algorithm is used to detect the change of the Dow Jones index data.According to the detected change points and the corresponding specific time,the causes of the change points are analyzed in detail.By using the Bayesian method to analyze the simulated data and the Dow Jones index data sequence,the change points in the sequence are successfully estimated,which provides some help for detecting the change points of the actual data.