Change points detection and parameter estimation for multivariate time series

In this paper, we propose a method to estimate the number and locations of change points and further estimate parameters of different regions for piecewise stationary vector autoregressive models. The procedure decomposes the problem of change points detection and parameter estimation along the component series. By reformulating the change point detection problem as a variable selection one, we apply group Lasso method to estimate the change points initially. Then, from the preliminary estimate of change points, a subset is selected based on the loss functions of Lasso method and a backward elimination algorithm. Finally, we propose a Lasso + OLS method to estimate the parameters in each segmentation for high-dimensional VAR models. The consistent properties of the estimation for the number and the locations of the change points and the VAR parameters are proved. Simulation experiments and real data examples illustrate the performance of the method.