| In the current global context of economic integration,unexpected events have an important influence in the financial field.This year,"COVID-19" outbreak has triggered financial turmoil in the whole country and even in the global market.In the tide of this era,how to sum up experience or predict future development through change-point detection is particularly important.It is an important part of today’s social development that methods of change-point detection are picked over and applied to different fields of life.In this thesis,four methods for detecting change-points are studied:likelihood ratio method,least square method,CUSUM method and local comparison method.Considering that Bernstein polynomials have worked well in density function approximation,the multidimensional Bernstein polynomials has been studied.We think of it as a finite linear combination of K known β distributions with coefficient pm.A convergent iterative form of its coefficients pm can be obtained by using EM algorithm.Different change-point estimating methods for choosing the optimal degree mj of the multidimensional Bernstein polynomials are used.Then,the bivariate normal distribution model with single change-point in the mean is used to carry out numerical simulation.By changing the mean difference,it is found that the likelihood ratio method,the least square method and the CUSUM method combined with the multi-dimensional Bernstein log likelihood function are more significant than the local comparison method.And they are more practical without considering the length of local interval.Finally,"COVID-19" data,"S&P 500" and"SSE 50" index are used for change-point detection with good results.The development trend of the epidemic in China and the differences of stock price changes between China and the United States in the past three years have been found.It is analyzed that change-point detection plays an important role in identifying major crisis events and financial shocks. |
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