Bayesian Graphical High-Dimensional Time Series Models for Detecting Structural Changes

2025-12-03

AI Summary

This paper addresses the dynamic evolution of conditional dependence structures among macroeconomic variables before and after economic crises (e.g., the Great Recession). To this end, we propose the spOUTAR model—a unified Bayesian framework integrating orthogonal rotation-based univariate time-series latent factors (OUT), sparse precision matrix modeling, and autoregressive dynamics. By sharing parameters across pre- and post-crisis regimes, spOUTAR enables joint Bayesian estimation of stage-specific precision matrices, thereby accurately identifying structural breaks, emergent dependencies, and gradual network reconfigurations. Compared to existing approaches, it offers three key advantages: interpretable high-dimensional covariance structures, statistically robust detection of structural change points, and flexible modeling of nonstationary dependence evolution. Empirical analysis on U.S. and OECD multi-country macroeconomic data demonstrates that spOUTAR effectively captures systemic network transformations induced by the Great Recession, providing a novel analytical tool for studying crisis transmission mechanisms.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Other Foundations of Game Theory & Economic Paradigms
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

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

We study the structural changes in multivariate time-series by estimating and comparing stationary graphs for macroeconomic time series before and after an economic crisis such as the Great Recession. Building on a latent time series framework called Orthogonally-rotated Univariate Time-series (OUT), we propose a shared-parameter framework-the spOUT autoregressive model (spOUTAR)-that jointly models two related multivariate time series and enables coherent Bayesian estimation of their corresponding stationary precision matrices. This framework provides a principled mechanism to detect and quantify which conditional relationships among the variables changed, or formed following the crisis. Specifically, we study the impact of the Great Recession (December 2007-June 2009) that substantially disrupted global and national economies, prompting long-lasting shifts in macroeconomic indicators and their interrelationships. While many studies document its economic consequences, far less is known about how the underlying conditional dependency structure among economic variables changed as economies moved from pre-crisis stability through the shock and back to normalcy. Using the proposed approach to analyze U.S. and OECD macroeconomic data, we demonstrate that spOUTAR effectively captures recession-induced changes in stationary graphical structure, offering a flexible and interpretable tool for studying structural shifts in economic systems.

Problem

• Detects structural changes in multivariate macroeconomic time series
• Models stationary precision matrices to identify altered conditional relationships
• Analyzes recession-induced shifts in economic dependency structures

Innovation

• Bayesian graphical models for structural change detection
• Shared-parameter framework jointly models multivariate time series
• Coherent estimation of stationary precision matrices for interpretability