Bayesian Dynamic Tensor Regression

Monica Billio; Roberto Casarin; Matteo Iacopini; Sylvia Kaufmann

doi:10.1080/07350015.2022.2032721

Bayesian Dynamic Tensor Regression

Monica Billio, Roberto Casarin, Matteo Iacopini, Sylvia Kaufmann

Research output: Contribution to Journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	429-439
Number of pages	11
Journal	Journal of Business & Economic Statistics
Volume	41
Issue number	2
Early online date	21 Mar 2022
DOIs	https://doi.org/10.1080/07350015.2022.2032721
Publication status	Published - 2023

Funding

This research used the SCSCF and HPC multiprocessor cluster systems and is part of the project Venice Center for Risk Analytics (VERA) at Ca\u2019 Foscari University of Venice. Monica Billio and Roberto Casarin acknowledge financial support from the Italian Ministry MIUR under the PRIN project Hi-Di NET\u2013Econometric Analysis of High Dimensional Models with Network Structures in Macroeconomics and Finance (grant agreement no. 2017TA7TYC). Matteo Iacopini acknowledges financial support from the EU Horizon 2020 programme under the Marie Sk\u0142odowska-Curie scheme (grant agreement no. 887220). We are grateful to Federico Bassetti, Sylvia Fr\u00FChwirth-Schnatter, Christian Gouri\u00E9roux, S\u00F8ren Johansen, Siem Jan Koopman, Gary Koop, Andr\u00E9 Lucas, Alain Monfort, Peter Phillips, Raquel Prado, Christian P. Robert, Mark Steel, and Mike West for their comments and suggestions. Also, we thank the seminar participants at Queen Mary University, CREST, University of Warwick, University of Southampton, Vrije University of Amsterdam, London School of Economics, Maastricht University, and Polytechnic University of Milan. We thank the participants at \u201CES Annual Meeting\u201D in Milan (2020), \u201CICEEE\u201D in Lecce (2019), \u201CCFENetwork\u201D in Pisa (2018), \u201CEC2\u201D in Rome (2018), \u201CRCEA Annual meeting\u201D in Rimini (2018), \u201CCFENetwork\u201D in London (2017), \u201CICEEE\u201D in Messina (2017), \u201CVienna Workshop on High-dimensional Time Series in Macroeconomics and Finance\u201D in Wien (2017), \u201CBISP10\u201D in Milan (2017), \u201CESOBE\u201D in Venice (2016), \u201CCFENetwork\u201D in Seville (2016), for their constructive comments.

Funders	Funder number
London School of Economics, Maastricht University
Università Ca' Foscari Venezia
University of Warwick
Horizon 2020 Framework Programme
Vrije University of Amsterdam
University of Southampton
Core Research for Evolutional Science and Technology
Queen Mary University
Polytechnic University of Milan
SCSCF
Italian Ministry MIUR	2017TA7TYC
Marie Skłodowska-Curie scheme	887220

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author = "Monica Billio and Roberto Casarin and Matteo Iacopini and Sylvia Kaufmann",

year = "2023",

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Bayesian Dynamic Tensor Regression

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