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

TL;DR

This paper introduces a Bayesian framework for detecting structural changes in high-dimensional macroeconomic time series by modeling and comparing their stationary graphical structures before and after economic crises.

Contribution

It proposes the spOUTAR model, a novel Bayesian method for jointly analyzing related multivariate time series and identifying changes in their conditional dependency structures.

Findings

Effectively captures recession-induced changes in economic variables.

Provides a flexible, interpretable tool for structural shift analysis.

Demonstrates success on U.S. and OECD macroeconomic data.

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.