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.

翻译：大型社交或金融网络中的个体或公司常因多种原因展现出显著异质性行为。本文提出一种具有潜在群体结构的网络向量自回归模型，用于建模网络节点观测到的异质性动态模式，该模型可自然融入群体层面的网络效应与时不变固定效应。在该框架下，通过最小化最小二乘型目标函数，可同步估计模型参数与网络节点归属。特别地，我们的理论分析允许在实现模型参数与群体归属估计一致性时，潜在群体数量G被过度设定，这显著提升了所提方法的鲁棒性。当G被正确设定时，基于估计量的渐近正态性可对模型参数进行有效统计推断。本文还开发了数据驱动准则以在实际应用中一致识别真实群体数量。通过大量模拟研究与两个真实数据案例验证了所提方法的有效性。