Testing Stability in Functional Event Observations with an Application to IPO Performance
针对仅在事件发生时才能观测到的函数型数据（如公司IPO后的股价轨迹），提出两步变点分析方法：先分割事件频率同质时段，再检验和估计函数均值的变点，并用蒙特卡洛模拟和IPO数据验证。
Many sequentially observed functional data objects are available only at the times of certain events. For example, the trajectory of stock prices of companies after their initial public offering (IPO) can be observed when the offering occurs, and the resulting data may be affected by changing circumstances. It is of interest to investigate whether the mean behavior of such functions is stable over time, and if not, to estimate the times at which apparent changes occur. Since the frequency of events may fluctuates over time, we propose a change point analysis that has two steps. In the first step, we segment the series into segments in which the frequency of events is approximately homogeneous using a new binary segmentation procedure for event frequencies. After adjusting the observed curves in each segment based on the frequency of events, we proceed in the second step by developing a method to test for and estimate change points in the mean of the observed functional data objects. We establish the consistency and asymptotic distribution of the change point detector and estimator in both steps, and study their performance using Monte Carlo simulations. An application to IPO performance data illustrates the proposed methods.