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.

在本文中，我们提出了一种方法，用于估计分段固定矢量自回归模型的变化点的数量和位置，并进一步估计不同区域的参数。该过程分解了沿组件系列的变化点检测和参数估计的问题。通过将变更点检测问题重新构造为变量选择变量，我们应用组Lasso方法初步估计变更点。然后，根据变化点的初步估计，基于Lasso方法的损失函数和后向消除算法选择一个子集。最后，我们提出了一种Lasso + OLS方法来估计高维VAR模型每个细分中的参数。证明了变化点的数量和位置以及VAR参数的估计的一致性质。仿真实验和实际数据示例说明了该方法的性能。