The Cointegrated Matrix Autoregressive Model

2026-04-01

AI Summary

Traditional econometric approaches treat observational data as vectors, making it difficult to effectively capture the two-dimensional structure of matrix-valued data and its intrinsic long-run equilibrium relationships. This study proposes a novel matrix cointegrated error correction model that, for the first time, establishes a cointegration framework admitting an equivalent matrix autoregressive (MAR) representation. By preserving the native matrix form of the data, the model naturally accommodates both cointegrating relationships and dynamic adjustment mechanisms. It accurately characterizes long-run equilibria and short-run dynamics among variables while maintaining structural integrity, thereby offering both economic interpretability and methodological innovation.

Abstract

Traditional econometric analyzes represent observations as vectors despite the inherent complexity of empirical data structures. When data are organized along dual classification dimensions, a matrix representation provides a more natural and interpretable framework. Building on recent advances in matrix autoregressive (MAR) modeling, this study introduces a novel error correction representation tailored for matrix-structured data. Through comparative analysis with existing methodologies, we demonstrate two critical advancements. First, the proposed model preserves the interpretative foundations of conventional cointegration analysis, with coefficients that explicitly capture dynamics rooted in adjustment toward steady-state positions. Second, in contrast to previous formulations, our error correction framework allows for an equivalent matrix autoregressive representation, preserving the fundamental structure of the data in both specifications. This ensures that the matrix representation reflects an intrinsic characteristic of the data.

Problem

• matrix autoregressive
• cointegration
• error correction model
• matrix-valued time series
• data structure

Innovation

• matrix autoregressive
• cointegration
• error correction model
• matrix-valued time series
• structural preservation