Learning coherent Granger-causality in panel vector autoregressive models

We consider the problem of forecasting multiple time series across multiple cross-sections based solely on the past observations of the series. We propose to use panel vector autoregressive model to capture the inter-dependencies on the past values of the multiple series. We restrict the panel vector autoregressive model to exclude the cross-sectional relationships and propose a method to learn models with sparse Granger-causality structures coherent across the panel sections. The method extends the concepts of group variable selection and support union recovery into the panel setting by extending the group lasso penalty (Yuan & Lin, 2006) into matrix output regression setting with 3d-tensor of model parameters.