  In this paper, we propose a new Granger causality measure which is robust
against the confounding influence of latent common inputs. This measure is
inspired by partial Granger causality in the literature, and its variant. Using
numerical experiments we first show that the test statistics for detecting
directed interactions between time series approximately obey the
$F$-distributions when there are no interactions. Then, we propose a practical
procedure for inferring directed interactions, which is based on the idea of
multiple statistical test in situations where the confounding influence of
latent common inputs may exist. The results of numerical experiments
demonstrate that the proposed method successfully eliminates the influence of
latent common inputs while the normal Granger causality method detects spurious
interactions due to the influence of the confounder.
