We develop a functional learning approach to modelling systems of time series which preserves the ability of standard linear time-series models (VARs) to uncover the Granger-causality links in between the series of the system while allowing for richer functional relationships. We propose a framework for learning multiple output-kernels associated with multiple input-kernels over a structured input space and outline an algorithm for simultaneous learning of the kernels with the model parameters with various forms of regularization including non-smooth sparsity inducing norms. We present results of synthetic experiments illustrating the benefits of the described approach.