This paper proposes a dynamic network framework for uncovering latent community paths in high-dimensional VAR-type models. By embedding a degree-corrected stochastic co-blockmodel (ScBM) into the transition matrices of VAR-type systems, we separate sending and receiving roles at the node level and summarize complex directional dependence in an interpretable low-dimensional form. Our method integrates directed spectral co-clustering with eigenvector smoothing to track how directional groups split, merge, or persist over time. This framework accommodates both periodic VAR (PVAR) models for cyclical seasonal evolution and generalized VHAR models for structural transitions across ordered dependence horizons. We establish non-asymptotic misclassification bounds for both procedures and provide supporting evidence through Monte Carlo experiments. Applications to U.S.\ nonfarm payrolls distinguish a recurrent business-centered core from more mobile, seasonally sensitive sectors. In global stock volatilities, the results reveal a compact U.S.-centered long-horizon block, a Europe-heavy developed core, and a more dynamic short-horizon reallocation of peripheral and bridge markets.

翻译：本文提出了一种动态网络框架，用于在高维VAR类型模型中揭示潜在社区路径。通过将基于度修正的随机协同块模型（ScBM）嵌入VAR类型系统的转移矩阵中，我们能够在节点层面区分发送与接收角色，并将复杂的方向依赖性概括为可解释的低维形式。我们的方法将定向谱协同聚类与特征向量平滑相结合，以追踪方向性群体随时间分裂、合并或持续的过程。该框架既适用于描述周期性季节演化的周期VAR（PVAR）模型，也适用于描述跨有序依赖时域结构转变的广义VHAR模型。我们为两种方法建立了非渐近误分类界，并通过蒙特卡洛实验提供了支持性证据。对美国非农就业数据的应用区分出一个以商业为中心的核心群体与更具流动性的季节性敏感部门。在全球股票波动率分析中，结果揭示了一个以美国为中心的紧凑型长期依赖块、一个以欧洲为主的发达核心，以及一个更具动态性的短期依赖重组区域，涉及边缘市场与桥接市场。