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In this paper, we propose a new Granger causality measure which is robustagainst the confounding influence of latent common inputs. This measure isinspired by partial Granger causality in the literature, and its variant. Usingnumerical experiments we first show that the test statistics for detectingdirected interactions between time series approximately obey the$F$-distributions when there are no interactions. Then, we propose a practicalprocedure for inferring directed interactions, which is based on the idea ofmultiple statistical test in situations where the confounding influence oflatent common inputs may exist. The results of numerical experimentsdemonstrate that the proposed method successfully eliminates the influence oflatent common inputs while the normal Granger causality method detects spuriousinteractions due to the influence of the confounder.

A new Granger causality measure for eliminating the confounding influence of latent common inputs