Nonparametric Multiple Change Point Detection for Non-Stationary Times Series

Abstract: This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral density functions are different. The theory is based on the assumption that within each segment, time series is a linear process, which means that our method works not only for classic time series models, e.g., causal and invertible ARMA process, but also preserves good performance for non-invertible moving average process. We show that our estimations for change points are consistent. Also, a Bayesian information criterion is applied to estimate the member of change points consistently. Simulation results as well as empirical results will be presented.