Simultaneous Estimation and Group Identification for Network Vector Autoregressive Model with Heterogeneous Nodes

We study the dynamic behaviors of heterogeneous individuals observed in a network.The heterogeneous dynamic patterns are characterized by a network vector autoregression model with a latent group structure, where group-wise network effects and time-invariant fixed-effects can be incorporated. A least-squares type objective function is proposed for simultaneous model estimation and group membership identification, and a computationally efficient algorithm is developed for the resulting non-convex optimization problem. Theoretical properties of the estimators are investigated, which allows the number of groups $G$ to be over-specified to achieve estimation consistency but requires a correctly specified $G$ for asymptotic normality. A data-driven selection criterion for $G$ is proposed and is shown to be consistent for identifying the true $G$. The effectiveness of the proposed model is demonstrated through extensive simulation studies as well as a real data example from Sina Weibo.