Non-parametric Wiener-Granger causality in partially observed systems

Wiener's definition of causality, commonly known as Wiener-Granger causality, has become a frequently used quantification of temporally resolved causality in numerous fields of science. In many empirical studies, the system of interest cannot be observed in its entirety and relevant information may reside outside of the sampled observations. To this end, partial Wiener-Granger causality has been developed to circumvent this issue. In this paper, we extend partial Wiener-Granger causality to the non-parametric case and discuss different approaches to estimate it.