Emanuele Lopetuso, Massimiliano Caporin
arXiv 1 Apr 2026 · Econometrics
arXiv:2604.00723 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Li, Zebang and Xiao, Han (2024) Cointegrated matrix autoregression models | 0.928 | 5 | 5 | 80% |
| 2 | Johansen, Søren (1995) Likelihood-based inference in cointegrated vector autoregressive models | 0.644 | 4 | 2 | 50% |
| 3 | Chen, Rong and Xiao, Han and Yang, Dan (2021) Autoregressive models for matrix-valued time series | 0.644 | 2 | 2 | 100% |
| 4 | Hecq, Alain and Ricardo, Ivan and Wilms, Ines (2025) Detecting cointegrating relations in non-stationary matrix-valued time series | 0.644 | 2 | 2 | 100% |
| 5 | Juselius, Katarina (2006) The cointegrated VAR model: methodology and applications | 0.511 | 2 | 2 | 50% |
| 6 | Anderson, Theodore Wilbur (1951) Estimating linear restrictions on regression coefficients for multivariate normal distributions | 0.405 | 1 | 1 | 100% |
| 7 | Billio, Monica and Casarin, Roberto and Costola, Michele and Iacopin… (2021) A matrix-variate t model for networks | 0.405 | 1 | 1 | 100% |
| 8 | Billio, Monica and Casarin, Roberto and Iacopini, Matteo and Kaufman… (2023) Bayesian dynamic tensor regression | 0.405 | 1 | 1 | 100% |
| 9 | Chen, Elynn Y and Chen, Rong (2019) Modeling dynamic transport network with matrix factor models: with an application to international trade flow | 0.405 | 1 | 1 | 100% |
| 10 | Chen, Elynn Y and Fan, Jianqing (2023) Statistical inference for high-dimensional matrix-variate factor models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.