The Cointegrated Matrix Autoregressive Model

TL;DR

This paper introduces a novel matrix autoregressive error correction model that enhances interpretability and structural preservation in analyzing matrix-structured econometric data.

Contribution

It develops a new error correction framework for MAR models that maintains interpretability and structural integrity of matrix data.

Findings

Model preserves interpretative foundations of cointegration analysis.

Framework allows for an equivalent matrix autoregressive representation.

Demonstrates advantages through comparative analysis.

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.