Large Bayesian Tensor Autoregressions

TL;DR

This paper develops a Bayesian tensor autoregressive model for analyzing large multidimensional time series data, such as international trade, incorporating stochastic volatility and efficient computation techniques.

Contribution

It introduces a novel Bayesian tensor autoregressive framework with stochastic volatility and low-rank Tucker decomposition for large-scale multidimensional time series analysis.

Findings

Captures time-varying volatility in trade data.

Provides a factor interpretation of complex tensor data.

Efficiently handles high-dimensional datasets with hierarchical shrinkage.

Abstract

The availability of multidimensional economic datasets has grown significantly in recent years. An example is bilateral trade values across goods among countries, comprising three dimensions -- importing countries, exporting countries, and goods -- forming a third-order tensor time series. This paper introduces a general Bayesian tensor autoregressive framework to analyze the dynamics of large, multidimensional time series with a particular focus on international trade across different countries and sectors. Departing from the standard homoscedastic assumption in this literature, we incorporate flexible stochastic volatility into the tensor autoregressive models. The proposed models can capture time-varying volatility due to the COVID-19 pandemic and recent outbreaks of war. To address computational challenges and mitigate overfitting, we develop an efficient sampling method based on low-rank Tucker decomposition and hierarchical shrinkage priors. Additionally, we provide a factor interpretation of the model showing how the Tucker decomposition projects large-dimensional disaggregated trade flows onto global factors.