This paper considers the problem of testing and estimation of change point where signals after the change point can be highly irregular, which departs from the existing literature that assumes signals after the change point to be piece-wise constant or vary smoothly. A two-step approach is proposed to effectively estimate the location of the change point. The first step consists of a preliminary estimation of the change point that allows us to obtain unknown parameters for the second step. In the second step we use a new procedure to determine the position of the change point. We show that, under suitable conditions, the desirable $\mathcal{O}_P(1)$ rate of convergence of the estimated change point can be obtained. We apply our method to analyze the Baidu search index of COVID-19 related symptoms and find 8~December 2019 to be the starting date of the COVID-19 pandemic.

翻译：本文研究信号在变点后可能高度不规则情形下的变点检验与估计问题，这区别于现有文献中假定变点后信号为分段常数或平滑变化的研究框架。我们提出一种两步法来有效估计变点位置：第一步通过初步估计获取变点位置的初始值，从而为第二步提供未知参数的估计；第二步采用新提出的程序确定变点的精确位置。在适当条件下，我们证明所估计的变点能达到理想的$\mathcal{O}_P(1)$收敛速率。我们将该方法应用于百度搜索指数中COVID-19相关症状的分析，发现2019年12月8日是COVID-19大流行的起始日期。