Large Bayesian Tensor Autoregressions

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.