  Our goal is to estimate causal interactions in multivariate time series.
Using vector autoregressive (VAR) models, these can be defined based on
non-vanishing coefficients belonging to respective time-lagged instances. As in
most cases a parsimonious causality structure is assumed, a promising approach
to causal discovery consists in fitting VAR models with an additional
sparsity-promoting regularization. Along this line we here propose that
sparsity should be enforced for the subgroups of coefficients that belong to
each pair of time series, as the absence of a causal relation requires the
coefficients for all time-lags to become jointly zero. Such behavior can be
achieved by means of l1-l2-norm regularized regression, for which an efficient
active set solver has been proposed recently. Our method is shown to outperform
standard methods in recovering simulated causality graphs. The results are on
par with a second novel approach which uses multiple statistical testing.
