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arXiv · 1709.09606

Bayesian Dynamic Tensor Regression

Monica Billio·Roberto Casarin·Matteo Iacopini·Sylvia Kaufmann
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Abstract

Tensor-valued data are becoming increasingly available in economics and this calls for suitable econometric tools. We propose a new dynamic linear model for tensor-valued response variables and covariates that encompasses some well-known econometric models as special cases. Our contribution is manifold. First, we define a tensor autoregressive process (ART), study its properties and derive the associated impulse response function. Second, we exploit the PARAFAC low-rank decomposition for providing a parsimonious parametrization and to incorporate sparsity effects. We also contribute to inference methods for tensors by developing a Bayesian framework which allows for including extra-sample information and for introducing shrinking effects. We apply the ART model to time-varying multilayer networks of international trade and capital stock and study the propagation of shocks across countries, over time and between layers.

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Monica Billio, Roberto Casarin, Matteo Iacopini, Sylvia Kaufmann. 2017-09-27. Bayesian Dynamic Tensor Regression. https://arxiv.org/abs/1709.09606

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