Bayesian Dynamic Tensor Tegression

Abstract:

Tensor-valued data (i.e. multidimensional data) are becoming increasingly available and call for suitable econometric tools. We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well-known multivariate models as special cases. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parametrization and to incorporate sparsity effects. Our contribution is twofold: first, we extend multivariate econometric models to account for tensor-valued response and covariates; second, we define a tensor autoregressive process (TAR) and the associated impulse response function for studying shock propagation. Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We apply the TAR model for studying time-varying multilayer economic networks concerning international trade and international capital stocks. We provide an impulse response analysis for assessing propagation of trade and financial shocks across countries, over time and between layers.

Co-authors: Roberto Casarin, Matteo Iacopini and Sylvia Kaufmann