Bayesian Dynamic Tensor Regression. Issue 2 (3rd April 2023)

• Record Type: Journal Article
• Authors: Billio, Monica; Casarin, Roberto; Iacopini, Matteo; Kaufmann, Sylvia
• Is Part Of: Journal of business & economic statistics. Volume 41:Issue 2(2023)
• Page Start: 429
• Page End: 439
• Publication Date: 2023-04-03
• Subjects: Bayesian inference -- Dynamic networks -- Forecasting -- Multidimensional autoregression -- Tensor models; Economics -- Statistical methods -- Periodicals; Commercial statistics -- Periodicals; Économie politique -- Méthodes statistiques -- Périodiques; Statistique commerciale -- Périodiques; 330.015195
• DOI: 10.1080/07350015.2022.2032721
• Languages: English
• ISSNs: 0735-0015

Abstract

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.