Identifying network Granger causality in large vector autoregressive (VAR) models enhances explanatory power by capturing complex interdependencies among variables. Instead of constructing network structures solely through sparse estimation of coefficients, we explore latent community structures to uncover the underlying network dynamics. We propose a dynamic network framework that embeds directed connectivity within the transition matrices of VAR-type models, enabling tracking of evolving community structures over time. To incorporate network directionality, we employ degree-corrected stochastic co-block models for each season or cycle, integrating spectral co-clustering with singular vector smoothing to refine latent community transitions. For greater model parsimony, we adopt periodic VAR (PVAR) and vector heterogeneous autoregressive (VHAR) models as alternatives to high-lag VAR models. We provide theoretical justifications for the proposed methodology and demonstrate its effectiveness through applications to the cyclic evolution of US nonfarm payroll employment and the temporal progression of realized stock market volatilities. Indeed, spectral co-clustering of directed networks reveals dynamic latent community trajectories, offering deeper insights into the evolving structure of high-dimensional time series.

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，能够通过捕捉变量间复杂的相互依赖关系来增强解释力。我们并非仅通过系数的稀疏估计来构建网络结构，而是探索潜在社区结构以揭示底层网络动态。本文提出一种动态网络框架，将有向连接性嵌入VAR类模型的转移矩阵中，从而实现对随时间演化的社区结构的追踪。为纳入网络方向性，我们针对每个季节或周期采用度校正随机协同块模型，将谱协同聚类与奇异向量平滑相结合，以优化潜在社区转移过程。为提升模型简约性，我们采用周期性VAR（PVAR）和向量异质自回归（VHAR）模型作为高滞后阶VAR模型的替代方案。我们为所提方法提供了理论论证，并通过美国非农就业数据的周期性演变与已实现股票市场波动率的时间进程两个应用案例验证了其有效性。研究表明，有向网络的谱协同聚类能够揭示动态的潜在社区轨迹，为高维时间序列的演化结构提供更深刻的洞见。