  Individuals or companies in a large social or financial network often display
rather heterogeneous behaviors for various reasons. In this work, we propose a
network vector autoregressive model with a latent group structure to model
heterogeneous dynamic patterns observed from network nodes, for which
group-wise network effects and timeinvariant fixed-effects can be naturally
incorporated. In our framework, the model parameters and network node
memberships can be simultaneously estimated by minimizing a least-squares type
objective function. In particular, our theoretical investigation allows the
number of latent groups G to be over-specified when achieving the estimation
consistency of the model parameters and group memberships, which significantly
improves the robustness of the proposed approach. When G is correctly
specified, valid statistical inference can be made for model parameters based
on the asymptotic normality of the estimators. A data-driven criterion is
developed to consistently identify the true group number for practical use.
Extensive simulation studies and two real data examples are used to demonstrate
the effectiveness of the proposed methodology.
