Identifying network Granger causality in large vector autoregressive (VAR) models enhances explanatory power by capturing complex dependencies among variables. This study proposes a methodology that explores latent community structures to uncover underlying network dynamics, rather than relying on sparse coefficient estimation for network construction. A dynamic network framework embeds directed connectivity in the transition matrices of VAR-type models, allowing the tracking of evolving community structures over time, called seasons. To account for network directionality, degree-corrected stochastic co-block models are fitted for each season, then a combination of spectral co-clustering and singular vector smoothing is utilized to refine transitions between latent communities. Periodic VAR (PVAR) and vector heterogeneous autoregressive (VHAR) models are adopted as alternatives to conventional VAR models for dynamic network construction. Theoretical results establish the validity of the proposed methodology, while empirical analyses demonstrate its effectiveness in capturing both the cyclic evolution and transient trajectories of latent communities. The proposed approach is applied to US nonfarm payroll employment data and realized stock market volatility data. Spectral co-clustering of multi-layered directed networks, constructed from high-dimensional PVAR and VHAR representations, reveals rich and dynamic latent community structures.

翻译：在大规模向量自回归（VAR）模型中识别网络格兰杰因果关系，通过捕捉变量间的复杂依赖关系提升了模型的解释力。本研究提出一种方法，旨在发掘潜在社区结构以揭示底层网络动态，而非依赖稀疏系数估计进行网络构建。通过动态网络框架将VAR型模型转移矩阵中的有向连接嵌入其中，从而能够追踪随时间演变的社区结构（称为季节）。为处理网络方向性，我们对每个季节拟合了度修正的随机共块模型，随后利用谱联合聚类与奇异向量平滑技术优化潜在社区间的过渡。采用周期VAR（PVAR）与向量异质自回归（VHAR）模型作为传统VAR模型的替代方案进行动态网络构建。理论结果验证了所提方法的有效性，而实证分析则展示了其在捕捉潜在社区的周期性演化与暂态轨迹方面的能力。将该方法应用于美国非农就业人口数据与已实现股市波动率数据。基于高维PVAR和VHAR表示构建的多层有向网络的谱联合聚类，揭示了丰富且动态的潜在社区结构。