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

Abstract

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 one-change-point detecting statistic, which covers a wide class of popular methods, including cumulative sum process, outlier-robust rank statistics and order statistics. Neither robust and consistent estimation of nuisance parameters, selection of bandwidth parameters, nor pre-specification of the number of change points is required. The finite-sample performance shows that our proposal is size-accurate, robust against misspecification of the alternative hypothesis, and more powerful than existing methods. Case studies of NASDAQ option volume and Shanghai-Hong Kong Stock Connect turnover are provided.