Bayesian Dynamic Tensor Regression

TL;DR

This paper introduces a Bayesian dynamic tensor regression model that captures complex relationships in tensor-valued data, with applications to international trade and capital stock networks, offering new inference tools and low-rank decompositions.

Contribution

It develops a tensor autoregressive process, explores its properties, and integrates Bayesian inference with low-rank and sparsity structures for dynamic tensor data.

Findings

Model effectively captures shock propagation in international networks

Bayesian framework improves inference with extra-sample information

Low-rank decomposition enhances model parsimony and interpretability

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.