  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 for
the case of autocorrelated continuous variables while keeping false positives
at the desired level. This performance gain grows with stronger
autocorrelation. At https://github.com/jakobrunge/tigramite we provide Python
code for all methods involved in the simulation studies.
