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 with latent variables, and provide a constrained-based causal feature selection method, which we prove that is both sound and complete under some graph constraints. Our theory and estimation algorithm require only 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. Furthermore, our selection of the conditioning set is such that it improves signal to noise ratio. We apply our method on real data, and on a wide range of simulated experiments, which yield very low false positive and relatively low false negative rates. * Since there can only be one target time series Y , by overloading the notation, we use Q to refer to X or U when we already refer to target's nodes by Y (Fig. 1).