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The Cointegrated Matrix Autoregressive Model

Emanuele Lopetuso, Massimiliano Caporin

arXiv 1 Apr 2026 · Econometrics

arXiv:2604.00723 · PDF · DOI · OpenAlex · Extracted main text

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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Li, Zebang and Xiao, Han (2024) Cointegrated matrix autoregression models0.9285580%
2Johansen, Søren (1995) Likelihood-based inference in cointegrated vector autoregressive models0.6444250%
3Chen, Rong and Xiao, Han and Yang, Dan (2021) Autoregressive models for matrix-valued time series0.64422100%
4Hecq, Alain and Ricardo, Ivan and Wilms, Ines (2025) Detecting cointegrating relations in non-stationary matrix-valued time series0.64422100%
5Juselius, Katarina (2006) The cointegrated VAR model: methodology and applications0.5112250%
6Anderson, Theodore Wilbur (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions0.40511100%
7Billio, Monica and Casarin, Roberto and Costola, Michele and Iacopin… (2021) A matrix-variate t model for networks0.40511100%
8Billio, Monica and Casarin, Roberto and Iacopini, Matteo and Kaufman… (2023) Bayesian dynamic tensor regression0.40511100%
9Chen, Elynn Y and Chen, Rong (2019) Modeling dynamic transport network with matrix factor models: with an application to international trade flow0.40511100%
10Chen, Elynn Y and Fan, Jianqing (2023) Statistical inference for high-dimensional matrix-variate factor models0.40511100%

Showing the top 10 of 23 scored citations.