Change point estimation for high-dimensional time series with network structure

High-dimensional datasets with a network structure are increasingly popular in various fields, such as sociology, finance, and bioinformatics. Existing research focuses on the stationary setting. This paper builds a change point model in which the high-dimensional time series is assumed to follow an autoregressive process with network effect within each time segment. In addition to the heterogeneous model with node-specific coefficients, the homogeneous and the grouped model, which assume different levels of homogeneity among model parameters, are also analyzed. A computationally efficient two-step procedure based on the fused LASSO and a general information criterion is developed to estimate the number and locations of change points simultaneously, as well as model parameters in each time segment. For the grouped model, after the identification of change points, a similar two-step procedure is employed to estimate the group structure for each time segment. The consistency of the proposed method for the number and locations of change points, the model parameters, and the group structure are established. Simulation and real data analysis on U.S. stock returns support the effectiveness of the proposed method in modeling high-dimensional network time series with structural breaks.