Latent Community Paths in VAR‐Type Models via Dynamic Directed Spectral Co‐Clustering

This paper proposes a dynamic network framework for uncovering latent community trajectories in high‐dimensional vector autoregressive (VAR)‐type models. The framework accommodates both periodic VAR (PVAR) models, which capture cyclical seasonal evolution, and generalized vector heterogeneous autoregressive (VHAR) models, which characterize structural transitions across ordered dependence horizons. By embedding a degree‐corrected stochastic co‐blockmodel into the transition matrices of these VAR‐type models, the proposed framework separates node‐level sending and receiving roles and summarizes directional and temporal dependence in an interpretable low‐dimensional representation. The proposed method integrates transition matrix estimation, directed spectral co‐clustering, and eigenvector smoothing to track how directional communities split, merge, or persist over time. Non‐asymptotic misclassification bounds are established for both PVAR‐ and generalized VHAR‐based networks, and Monte Carlo experiments support the theoretical results. Application to U.S. nonfarm payroll data using the PVAR‐based framework reveals a recurrent business‐centered core alongside more mobile, seasonally sensitive sectors. Application to global stock volatility data using the VHAR‐based framework identifies a compact U.S.‐centered long‐horizon block, a Europe‐dominated developed‐market core, and a more dynamic short‐horizon reallocation of peripheral and bridge markets.