Multiple Change Points Detection in Low Rank and Sparse High Dimensional Vector Autoregressive Models

Identifying change/break points in multivariate time series represents a canonical problem in signal processing, due to numerous applications related to anomaly detection problems. The underlying detection methodology heavily depends on the nature of the mechanism determining the temporal dynamics of the data. Vector auto-regressive models (VAR) constitute a widely used model in diverse areas, including surveillance applications, economics/finance and neuroscience. In this work, we consider piece-wise stationary VAR models exhibiting break points between the corresponding stationary segments, wherein the transition matrices that govern the model's temporal evolution are decomposed into a common low-rank component and time evolving sparse ones. Further, we assume that the number of available time points are smaller than the number of model parameters and hence we are operating in a high-dimensional regime. We develop a three-step strategy that accurately detects the number of change points together with their location and subsequently estimates the model parameters in each stationary segment. The effectiveness of the proposed procedure is illustrated on both synthetic and real data sets.