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

2026-04-14

AI Summary

This study addresses the challenge of modeling directional dependencies in dynamic community evolution within high-dimensional vector autoregressive (VAR) frameworks. The authors propose a novel approach that embeds a degree-corrected stochastic co-blockmodel into the VAR transition matrix, thereby distinguishing between nodes’ sending and receiving roles for the first time within a VAR setting. By integrating dynamic directed spectral co-clustering with eigenvector smoothing techniques, the method effectively tracks time-varying community structures while accommodating both periodic and structural dependencies. Theoretical analysis yields non-asymptotic misclassification bounds. Empirical applications reveal stable core sectors and seasonally sensitive industries in U.S. nonfarm payroll data, and uncover a U.S.-centric persistent block, a European-led developed-market core, and a dynamically reallocating peripheral market in global equity volatility.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

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.

Problem

• latent community paths
• VAR-type models
• dynamic directed networks
• spectral co-clustering
• time-varying community structure

Innovation

• dynamic directed spectral co-clustering
• stochastic co-blockmodel
• VAR-type models
• eigenvector smoothing
• latent community paths