Necessary and sufficient conditions for causal feature selection in time series with latent common causes

We study the identification of direct and indirect causes on time series and provide necessary and sufficient conditions in the presence of latent variables. Our theoretical results and estimation algorithms require two conditional independence tests for each observed candidate time series to determine whether or not it is a cause of an observed target time series. We provide experimental results in simulations, where the ground truth is known, as well as in real data. Our results show that our method leads to essentially no false positives and relatively low false negative rates, even in confounded environments with non-unique lag effects, outperforming the widely used Granger causality and two more methods.