Learning vector autoregressive models with focalised Granger-causality graphs

While the importance of Granger-causal (G-causal) relationships for learning vector autoregressive models (VARs) is widely acknowledged, the state-of-the-art VAR methods do not address the problem of discovering the underlying G-causality structure in a principled manner. VAR models can be restricted if such restrictions are supported by a strong domain theory (e.g. economics), but without such strong domain-driven constraints the existing VAR methods typically learn fully connected models where each series is G-caused by all the others. We develop new VAR methods that address the problem of discovering structure in the G-causal relationships explicitly. Our methods learn sparse G-causality graphs with small sets of \emph{focal} series that govern the dynamical relationships within the time-series system. While maintaining competitive forecasting accuracy, the sparsity in the G-causality graphs that our methods achieve is far from reach of any of the state-of-the-art VAR methods.