Bayesian Dynamic Tensor Regression

64 Pages Posted: 8 Jun 2018

See all articles by Monica Billio

Monica Billio

Ca Foscari University of Venice - Dipartimento di Economia

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Sylvia Kaufmann

Independent

Matteo Iacopini

Ca Foscari University of Venice

Date Written: May 24, 2018

Abstract

Multidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools. We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well-known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases. For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, we exploit a suitable parametrization based on the parallel factor (PARAFAC) decomposition which enables to achieve both parameter parsimony and to incorporate sparsity effects. Our contribution is twofold: first, we provide an extension of multivariate econometric models to account for both tensor-variate response and covariates; second, we show the effectiveness of proposed methodology in defining an autoregressive process for time-varying real economic networks. Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We show the efficiency of the MCMC procedure on simulated datasets, with different size of the response and independent variables, proving computational efficiency even with high-dimensions of the parameter space. Finally, we apply the model for studying the temporal evolution of real economic networks.

Keywords: Tensor calculus, tensor decomposition, Bayesian statistics, hierarchical prior, networks, autoregessive model, time series, international trade

JEL Classification: C13, C33, C51, C53

Suggested Citation

Billio, Monica and Casarin, Roberto and Kaufmann, Sylvia and Iacopini, Matteo, Bayesian Dynamic Tensor Regression (May 24, 2018). University Ca' Foscari of Venice, Dept. of Economics Research Paper Series No. 13/WP/2018, Available at SSRN: https://ssrn.com/abstract=3192340 or http://dx.doi.org/10.2139/ssrn.3192340

Monica Billio

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

HOME PAGE: http://www.unive.it/persone/billio

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics ( email )

San Giobbe 873/b
Venice, 30121
Italy
+39 030.298.91.49 (Phone)
+39 030.298.88.37 (Fax)

HOME PAGE: http://sites.google.com/view/robertocasarin

Sylvia Kaufmann

Independent

Matteo Iacopini (Contact Author)

Ca Foscari University of Venice ( email )

Dorsoduro 3246
Venice, Veneto 30123
Italy

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