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Bayesian Dynamic Tensor Regression

Author

Listed:
  • Monica Billio
  • Roberto Casarin
  • Matteo Iacopini
  • Sylvia Kaufmann

Abstract

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors and call for appropriate statistical tools. We propose a new linear autoregressive tensor process (ART) for tensor-valued data, that encompasses some well-known time series models as special cases. We study its properties and derive the associated impulse response function. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parameterization and develop a Bayesian inference allowing for shrinking effects. We apply the ART model to time series of multilayer networks and study the propagation of shocks across nodes, layers and time.

Suggested Citation

  • Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    • Handle: RePEc:taf:jnlbes:v:41:y:2023:i:2:p:429-439
    DOI: 10.1080/07350015.2022.2032721
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    File URL: http://hdl.handle.net/10.1080/07350015.2022.2032721
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    Citations

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    Cited by:

    1. Billio, Monica & Casarin, Roberto & Costola, Michele & Iacopini, Matteo, 2024. "COVID-19 spreading in financial networks: A semiparametric matrix regression model," Econometrics and Statistics, Elsevier, vol. 29(C), pages 113-131.
    2. Matteo Barigozzi & Luca Trapin, 2025. "Estimation of large approximate dynamic matrix factor models based on the EM algorithm and Kalman filtering," Papers 2502.04112, arXiv.org, revised Jan 2026.
    3. Emanuele Lopetuso & Massimiliano Caporin, 2026. "The Cointegrated Matrix Autoregressive Model," Papers 2604.00723, arXiv.org.
    4. Huang, Feiqing & Lu, Kexin & Zheng, Yao & Li, Guodong, 2025. "Supervised factor modeling for high-dimensional linear time series," Journal of Econometrics, Elsevier, vol. 249(PB).
    5. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    6. Monica Billio & Roberto Casarin & Fausto Corradin & Antonio Peruzzi, 2025. "Bayesian Outlier Detection for Matrix-variate Models," Papers 2503.19515, arXiv.org, revised Aug 2025.
    7. Casarin, Roberto & Craiu, Radu V. & Wang, Qing, 2025. "Markov switching multiple-equation tensor regressions," Journal of Multivariate Analysis, Elsevier, vol. 208(C).
    8. Monica Billio & Roberto Casarin & Fausto Corradin & Antonio Peruzzi, 2025. "Bayesian Outlier Detection for Matrix–variate Models," Working Papers 2025: 14, Department of Economics, University of Venice "Ca' Foscari".

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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