Non-Stationary Time-Series Segmentation Based on the Schur Prediction Error Analysis

This paper proposes a non-stationary time-series segmentation method based on the analysis of the forward prediction error issued from the adaptive Schur orthogonal signal parameterisation. There is no a priori information about the analysed signal thus this method can be easily adapted to a large family of different types of signals for which two different stochastic processes are present. We set out some of the advantages of the adaptive Schur filter in deducing the presence of different non-stationary transient or long-term events leading to the signal segmentation. For each sample, the adaptive Schur algorithm calculates the optimal second-order solution for the signal prediction resulting in a set of time-varying model parameters (inter alia forward prediction error). We define the likelihood ratio (LR) test based on the Schur forward prediction error that is evaluated at each sample, thus giving excellent time-reaction properties. The LR test allows us to effectively partition the analysed time-series into homogeneous segments by considering its second-order statistics which are tracked adaptively by the Schur filter. The results performed by applying the proposed method to simulated signals are shown to verify its high performance