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.