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Bayesian Dynamic Tensor Regression

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  • 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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    Cited by:

    1. Billio Monica & Casarin Roberto & Costola Michele & Iacopini Matteo, 2021. "COVID-19 spreading in financial networks: A semiparametric matrix regression model," Papers 2101.00422, arXiv.org.

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    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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