Unsupervised Self-Normalized Change-Point Testing for Time Series

We propose a new self-normalized method for testing change points in the time series setting. Self-normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean. However, it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series, and its adaptation to change-point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power. Compared with existing results on using self-normalization in this direction, the current article proposes a new self-normalized change-point test that does not require prespecifying the number of total change points and is thus unsupervised. In addition, we propose a new contrast-based approach in generalizing self-normalized statistics to handle quantities other than the mean, which is specifically tailored for change-point testing. Monte Carlo simulations are presented to illustrate the finite-sample performance of the proposed method. Supplementary materials for this article are available online.