基于CUSUM方法的百度指数变点分析
Baidu Index Change Point Analysis Based on CUSUM Method

本文主要介绍了CUSUM方法的均值与方差变点估计且该方法对数据的分布限制较少，模拟了CUSUM方法对服从正态分布的时间序列数据以及非正态分布时间序列数据的变点估计，该方法都能准确估计变点的位置，且与实际相符合。对于收集到的“新冠”百度指数时间序列(只存在一个变点)数据应用CUSUM的均值和方差变点估计方法进行变点估计，结果表明均值变点和方差估计方法对“新冠”百度指数的时间序列数据的变点估计都是准确的。然而对于“房贷利率”百度指数时间序列数据(存在两个变点)，需要结合CUSUM方法的递归算法进行变点位置估计；估计到的变点位置与实际位置是相符的。同时对于估计到百度指数时间序列数据变点都具有很好的可解释性，都是符合实际情况的。
This paper mainly introduces the CUSUM method’s mean and variance change point estimation, which has fewer restrictions on the distribution of data. The CUSUM method’s change point estimation for time series data subject to normal distribution and non-normal distribution time series data is simulated. The method can accurately estimate the position of change points and is consistent with reality. For the collected time series data of the “new crown” Baidu index (only one variable point exists), CUSUM’s mean and variance variable point estimation methods are applied to estimate the variable points, and the results show that both the mean and variance estimation methods are accurate for the time series data of the “new crown” Baidu index. The results show that the mean and variance estimation methods are accurate for the time series data of “new crown” Baidu index. However, for “mortgage interest rate” Baidu index time series data (there are two change points), it is necessary to combine the recursive algorithm of the CUSUM method to estimate the change point location; The estimated position of the change point is consistent with the actual position. At the same time, it has good interpretability for estimating the change points of Baidu index time series data, and it is in line with the actual situation.