  We present a new method for forecasting systems of multiple interrelated time
series. The method learns the forecast models together with discovering leading
indicators from within the system that serve as good predictors improving the
forecast accuracy and a cluster structure of the predictive tasks around these.
The method is based on the classical linear vector autoregressive model (VAR)
and links the discovery of the leading indicators to inferring sparse graphs of
Granger causality. We formulate a new constrained optimisation problem to
promote the desired sparse structures across the models and the sharing of
information amongst the learning tasks in a multi-task manner. We propose an
algorithm for solving the problem and document on a battery of synthetic and
real-data experiments the advantages of our new method over baseline VAR models
as well as the state-of-the-art sparse VAR learning methods.
