Dynamic spectral co-clustering of directed networks to unveil latent community paths in VAR-type models

2025-02-15

AI Summary

Identifying Granger causality networks and dynamic communities in high-dimensional vector autoregressive (VAR) models remains challenging due to structural complexity and temporal heterogeneity. Method: We propose a directed network dynamic spectral co-clustering framework that jointly models structural evolution and causal dynamics. To this end, we first integrate the degree-corrected stochastic co-block model (DCSCM) with singular vector smoothing to capture time-varying directed network topology. We further incorporate periodic VAR (PVAR) and vector heterogeneous autoregression (VHAR) to enhance model parsimony and interpretability, supported by rigorous spectral convergence theory. Contribution/Results: Experiments on U.S. nonfarm payroll data uncover interpretable periodic community evolution paths, while analysis of stock market realized volatility reveals temporally resolved Granger causal transmission structures. The framework significantly improves dynamic structural insight and interpretability of high-dimensional VAR models—without compromising statistical rigor.

Technology Category

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

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
• Social Networks and Social Media: Computational social science

Abstract

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.

Problem

• Unveil latent community paths in VAR-type models
• Identify network Granger causality in large VAR models
• Track evolving community structures in directed networks

Innovation

• Dynamic spectral co-clustering for latent communities
• Degree-corrected stochastic co-block models for directionality
• PVAR and VHAR models for dynamic network construction