Group LASSO for multiple change-point detection in a generalized integer-valued autoregressive model

In this paper, we propose a computationally efficient and theoretically justified group least absolute shrinkage and selection operator (Group LASSO; GLASSO) method for estimating multiple change-points in a piecewise stationary generalized integer-valued autoregressive process. The proposed method is particularly suitable for finite samples with many closely spaced change-points. We further develop an efficient implementation that combines least angle regression and optimal partitioning (OP). The overall computational complexity is O(Kn+K2) when OP is used and O(Kn+K3) when the backward elimination algorithm is used. In addition, we propose an iterative procedure for selecting a data-driven order p~, which achieves satisfactory performance with relatively low computational cost. Simulation studies and a real data analysis demonstrate that the proposed method and iterative procedure perform well in practice and support the theoretical results.