Research
Research
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 homoskedastic assumption in this literature, we incorporate flexible stochastic volatility into the tensor autoregressive models. The proposed models could 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.
High-dimensional matrix-valued time-series are increasingly common in economics and finance. Prominent examples include large cross-region panels and dynamic economic networks. As the dimensions of the matrix grow, conventional approaches based on vector autoregressions-implemented by vectoring the matrix-valued databecome computationally infeasible. We introduce a class of large Bayesian matrix autoregressions (BMARs) that can accommodate time-varying volatility, nonGaussian errors and COVID-19 outliers. To tackle parameter proliferation, we propose Minnesota-type shrinkage priors on the MAR coefficients. We develop a unified approach for estimating this class of models, which scales well to high dimensions. The empirical relevance of these new BMARs is illustrated using a US state-level dataset that contains 6 macroeconomic times-series for each of the 50 states, with a total of 300 times-series.
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.
The limited availability of historical state-level GDP data poses significant challenges for macroeconomic analysis and forecasting. Traditional approaches often rely on alternative economic indicators, which may not fully capture economic activity. In this paper, we introduce a matrix variate framework to address missing data and mixed-frequency observations in state-level GDP modeling. Our framework leverages a set of sampling techniques to efficiently construct a Bayesian Markov Chain Monte Carlo (MCMC) algorithm for estimation and forecasting. We apply this method to two empirical applications: first, we generate historical quarterly state-level GDP estimates from 1988Q2 to 2004Q4 using seven state-level indicators available prior to 2005; second, we extend our framework to a mixed-frequency setting, incorporating monthly state-level indicators to produce high-frequency monthly GDP estimates. These applications highlight the advantages of our approach in capturing regional business cycles and improving forecasting accuracy. Our findings demonstrate that the matrix variate structure, combined with Bayesian inference, provides a robust solution for handling missing macroeconomic data while preserving key interdependencies in the data.