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

Alain Hecq, Ivan Ricardo and Ines Wilms

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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.

Date: 2025-09
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