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Large Bayesian matrix autoregressions

Author

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  • Chan, Joshua C.C.
  • Qi, Yaling

Abstract

High-dimensional matrix-valued time-series are increasingly common in economics and finance. Prominent examples include large cross-region panels and dynamic economic networks. As the dimensions of the matrix grow, conventional approaches based on vector autoregressions—implemented by vectoring the matrix-valued data—become computationally infeasible. We introduce a class of large Bayesian matrix autoregressions (BMARs) that can accommodate time-varying volatility, non-Gaussian errors and COVID-19 outliers. To tackle parameter proliferation, we propose Minnesota-type shrinkage priors on the MAR coefficients. We develop a unified approach for estimating this class of models, which scales well to high dimensions. The empirical relevance of these new BMARs is illustrated using a US state-level dataset that contains 6 macroeconomic times-series for each of the 50 states, with a total of 300 times-series.

Suggested Citation

  • Chan, Joshua C.C. & Qi, Yaling, 2026. "Large Bayesian matrix autoregressions," Journal of Econometrics, Elsevier, vol. 256(PB).
    • Handle: RePEc:eee:econom:v:256:y:2026:i:pb:s0304407625000090
    DOI: 10.1016/j.jeconom.2025.105955
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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