Decomposing Co-Movements in Matrix-Valued Time Series: A Pseudo-Structural Reduced-Rank Approach

2025-09-24

AI Summary

This paper addresses the structural decomposition of contemporaneous co-movement in matrix-valued time series. We propose a pseudo-structured reduced-rank autoregressive model that uniquely decomposes co-movement into three interpretable components—row effects, column effects, and row–column interaction effects—while preserving the intrinsic matrix structure. Methodologically, we embed this structural decomposition within a reduced-rank matrix autoregression framework and develop a BIC-type information criterion that jointly selects both the reduced rank and lag order, enabling standard asymptotic inference. Estimation proceeds via maximum likelihood under pseudo-structural constraints. Simulation studies demonstrate robust performance in parameter estimation accuracy, confidence interval coverage, and rank identification. Empirical applications to U.S. interstate economic indicators and cross-national macroeconomic data uncover clear, interpretable patterns of synchronized evolution.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Personalized content ranking and presentation
• 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

Abstract

We propose a pseudo-structural framework for analyzing contemporaneous co-movements in reduced-rank matrix autoregressive (RRMAR) models. Unlike conventional vector-autoregressive (VAR) models that would discard the matrix structure, our formulation preserves it, enabling a decomposition of co-movements into three interpretable components: row-specific, column-specific, and joint (row-column) interactions across the matrix-valued time series. Our estimator admits standard asymptotic inference and we propose a BIC-type criterion for the joint selection of the reduced ranks and the autoregressive lag order. We validate the method's finite-sample performance in terms of estimation accuracy, coverage and rank selection in simulation experiments, including cases of rank misspecification. We illustrate the method's practical usefelness in identifying co-movement structures in two empirical applications: U.S. state-level coincident and leading indicators, and cross-country macroeconomic indicators.

Problem

• Analyzing contemporaneous co-movements in matrix-valued time series data
• Decomposing co-movements into row-specific, column-specific, and joint interactions
• Preserving matrix structure unlike conventional vector-autoregressive models

Innovation

• Pseudo-structural framework preserves matrix structure in time series
• Decomposes co-movements into row, column, and joint components
• BIC-type criterion selects reduced ranks and lag order