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

## TL;DR

This paper introduces a new Granger causality measure that effectively removes the confounding effects of latent common inputs, improving the accuracy of detecting true directed interactions in time series data.

## Contribution

A novel Granger causality measure inspired by partial Granger causality that is robust against latent confounders, with a practical inference procedure demonstrated through numerical experiments.

## Key findings

- The test statistics follow F-distributions under no interaction.
- The proposed method eliminates false positives caused by latent confounders.
- Normal Granger causality detects spurious interactions due to confounders.

## Abstract

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.