Abstract: We propose a self-normalization sequential change-point detection method for time series. To test for parameter changes, most traditional sequential monitoring tests use a cumulative sum-based test statistic, which involves a long-run variance estimator. However, such estimators require choosing a bandwidth parameter, which may be sensitive to the performance of the test. Moreover, traditional tests usually suffer from severe size distortion as a result of the slow convergence rate to the limit distribution in the early monitoring stage. We propose self-normalization method to address these issues. We establish the null asymptotic and the consistency of the proposed sequential change-point test under general regularity conditions. Simulation experiments and an applications to railway-bearing temperature data illustrate and verify the proposed method.

Key words and phrases: ARMA-GARCH model, on-line detection, pairwise likelihood, quickest detection, sequential monitoring, stochastic volatility model.