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Bayesian Markov Switching Tensor Regression for Time-varying Networks

Monica Billio (), Roberto Casarin () and Matteo Iacopini ()

No 2018:14, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

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 (search for similar items in EconPapers)
JEL-codes: C13 C33 C51 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dcm, nep-ecm and nep-ore
Date: 2018
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