Study of Change-Point Detection and Applications Based on Several Statistical Methods

In the current global context of economic integration, unexpected events have an important influence in the financial field. In 2020, the "COVID-19" outbreak triggered financial turmoil throughout the whole country and even in the global market. In the wake of this era, how to sum up past developments and predict future development through change-point detection is particularly important. In this paper, four methods for detecting change-points are presented: the likelihood ratio method, least squares method, CUSUM method, and local comparison method. Considering that Bernstein polynomials have worked well in density function approximation, the multi-dimensional Bernstein polynomials are presented. The study applies multiple change-point detection methods to determine the most suitable degree of freedom mj for multi-dimensional Bernstein models, after which various rewriting expressions can be obtained. Next, "COVID-19" data and money supply data are used for change-point detection with good results. Then, we focus on conducting change-point testing on the S&P 500 index and SSE 50 index, indicating strong symmetry when major crisis events occur. All analyses indicate that change-point detection plays an important role in identifying major crisis events and financial shocks.