Bayesian Markov Switching Tensor Regression For Time-Varying Networks

63 Pages Posted: 8 Jun 2018

See all articles by Monica Billio

Monica Billio

University of Venice - Department of Economics; Ca Foscari University of Venice - Dipartimento di Economia

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Matteo Iacopini

Queen Mary University of London

Date Written: May 24, 2018

Abstract

We propose a new Bayesian Markov switching regression model for multi-dimensional arrays (tensors) of binary time series. We assume a zero-inflated logit dynamics with time-varying parameters and apply it to multi-layer temporal networks. The original contribution is threefold. First, in order to avoid over-fitting we propose a parsimonious parametrization of the model, based on a low-rank decomposition of the tensor of regression coefficients.

Second, the parameters of the tensor model are driven by a hidden Markov chain, thus allowing for structural changes. The regimes are identified through prior constraints on the mixing probability of the zero-inflated model. Finally, we model the jointly dynamics of the network and of a set of variables of interest. We follow a Bayesian approach to inference, exploiting the Pólya-Gamma data augmentation scheme for logit models in order to provide an efficient Gibbs sampler for posterior approximation. We show the effectiveness of the sampler on simulated datasets of medium-big sizes, finally we apply the methodology to a real dataset of financial networks.

Keywords: Tensor calculus, tensor decomposition, latent variables, Bayesian statistics, hierarchical prior, networks, zero-inflated model, time series, financial networks

JEL Classification: C13, C33, C51, C53

Suggested Citation

Billio, Monica and Billio, Monica and Casarin, Roberto and Iacopini, Matteo, Bayesian Markov Switching Tensor Regression For Time-Varying Networks (May 24, 2018). University Ca' Foscari of Venice, Dept. of Economics Research Paper Series No. 14/WP/2018 , Available at SSRN: https://ssrn.com/abstract=3192341 or http://dx.doi.org/10.2139/ssrn.3192341

Monica Billio

University of Venice - Department of Economics ( email )

Fondamenta San Giobbe 873
Venezia 30121
Italy
+39 041 234 9170 (Phone)
+39 041 234 9176 (Fax)

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

Matteo Iacopini (Contact Author)

Queen Mary University of London ( email )

Mile End Road
London, E1 4NS
United Kingdom

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