Bayesian Dynamic Tensor Regression

Monica Billio, Roberto Casarin, Matteo Iacopini, Sylvia Kaufmann

Research output: Contribution to JournalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)429-439
Number of pages11
JournalJournal of Business & Economic Statistics
Issue number2
Publication statusPublished - 2023


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