# Bayesian Dynamic Tensor Regression

arXiv: https://arxiv.org/abs/1709.09606 · HTML: https://mlsanity.com/paper/1709.09606/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2017.

## Built on by (most cited first, 1 of 1)

- [Bayesian Poisson-Randomized Gamma Tensor Factorization with Application to International Trade Flows](https://mlsanity.com/paper/2606.17267/) (2026)

## Abstract (arXiv)

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.