It allows for both latent confounders and selection variables, although in this paper we assume the absence of selection variables.

This performance gain grows with stronger autocorrelation.

It allows for both latent confounders and selection variables, although in this paper we assume the absence of selection variables.

We present a new method for linear and nonlinear, lagged and contemporaneous constraint-based causal discovery from observational time series in the presence of latent confounders. We show that existing causal discovery methods such as FCI and variants suffer from low recall in the autocorrelated time series case and identify low effect size of conditional independence tests as the main reason. Information-theoretical arguments show that effect size can often be increased if causal parents are included in the conditioning sets. To identify parents early on, we suggest an iterative procedure that utilizes novel orientation rules to determine ancestral relationships already during the edge removal phase. We prove that the method is order-independent, and sound and complete in the oracle case. Extensive simulation studies for different numbers of variables, time lags, sample sizes, and further cases demonstrate that our method indeed achieves much higher recall than existing methods while keeping false positives at the desired level. This performance gain grows with stronger autocorrelation. Our method also covers causal discovery for non-time series data as a special case. We provide Python code for all methods involved in the simulation studies.