Latent community paths in VAR-type models via dynamic directed spectral co-clustering

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.