A General Framework for Constructing Locally Self-Normalized Multiple-Change-Point Tests

We propose a general framework to construct self-normalized multiple-change-point tests with time series data. The only building block is a user-specified single-change-detecting statistic, which covers a large class of popular methods, including the cumulative sum process, outlier-robust rank statistics, and order statistics. The proposed test statistic does not require robust and consistent estimation of nuisance parameters, selection of bandwidth parameters, nor pre-specification of the number of change points. The finite-sample performance shows that the proposed test is size-accurate, robust against misspecification of the alternative hypothesis, and more powerful than existing methods. Case studies of the Shanghai-Hong Kong Stock Connect turnover are provided.本文提出一种面向时间序列数据的自归一化多变点检验构建通用框架。该框架仅以用户指定的单变点检测统计量作为唯一构建模块，可涵盖一大类主流方法，包括累积和过程、抗异常值秩统计量与次序统计量。所提出的检验统计量无需对冗余参数进行稳健且一致的估计、无需选择带宽参数，亦无需预先指定变点的数量。有限样本性能验证结果表明，所提检验具备尺度准确性，可对抗备择假设的设定误偏，且相较于现有方法拥有更优的检验功效。本文还提供了沪港通成交额的案例研究。