Large Bayesian Tensor VARs with Stochastic Volatility

TL;DR

This paper introduces Bayesian tensor VARs with low-rank tensor decomposition and stochastic volatility, demonstrating improved forecasting performance over standard Bayesian VAR models in US quarterly data.

Contribution

It develops a novel Bayesian tensor VAR framework with stochastic volatility, incorporating low-rank tensor decomposition for enhanced modeling of multivariate time series.

Findings

Tensor VARs outperform standard Bayesian VARs in forecasting accuracy.

Parsimonious stochastic volatility models forecast better than more flexible ones.

The proposed models effectively handle high-dimensional multivariate data.

Abstract

We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly variables, we show that these TVARs outperform the standard Bayesian VAR with the Minnesota prior. The results also suggest that the parsimonious common stochastic volatility model tends to forecast better than the more flexible Cholesky stochastic volatility model.