A Self-Normalized Approach to Sequential Change-point Detection for Time Series

This paper proposes a self-normalization sequential change-point detection method for time series. In testing for parameter changes, most of the traditional sequential monitoring tests utilize a CUSUM-based test statistic, which involves a long-run variance estimator. However, the commonly used long-run variance estimators require the choice of bandwidth parameter which could be sensitive to the performance. Moreover, the traditional tests usually suffer from severe size distortion due to the slow convergence rate to the limit distribution in the early monitoring stage. In this article, a self-normalization method is proposed to tackle these issues. We establish null asymptotic and the consistency of the proposed sequential change-point test under general regularity conditions. Simulation experiments and applications to railway bearing temperature data are conducted for illustrations. 1 Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)