  We study Granger causality in the context of wide-sense stationary time
series, where our focus is on the topological aspects of the underlying
causality graph. We establish sufficient conditions (in particular, we develop
the notion of a "strongly causal" graph topology) under which the true
causality graph can be recovered via pairwise causality testing alone, and
provide examples from the gene regulatory network literature suggesting that
our concept of a strongly causal graph may be applicable to this field. We
implement and detail finite-sample heuristics derived from our theory, and
establish through simulation the efficiency gains (both statistical and
computational) which can be obtained (in comparison to LASSO-type algorithms)
when structural assumptions are met.
