Sparse Graphical Vector Autoregression: A Bayesian Approach

In high-dimensional vector autoregressive (VAR) models, it is natural to have large number of predictors relative to the observations, and model selection is often a difficult issue. In this paper, we propose a model selection approach to multivariate time series of large dimension by combining graph-based notion of causality with the concept of sparsity on the structure of dependence among the variables. In particular, we build on the application of fan-in restriction for graphical models by proposing a sparsity-inducing prior distribution that allows for different prior information level about the maximal number of predictors for each equation of a VAR model. We discuss the joint inference of the temporal dependence in the observed series and the maximum lag order of the process, with the parameter estimation of the model. The applied contribution focuses on modeling and forecasting selected macroeconomic and financial time series with many predictors. Our result shows a gain in predictive performance using our sparse graphical VAR.