Discovering instantaneous and lagged causal relations in autocorrelated nonlinear time series datasets

The paper introduces a novel conditional in- dependence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suf- fer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI + , extends PCMCI [Runge et al., 2019b] to include discovery of contempo- raneous links. PCMCI + improves the relia- bility of CI tests by optimizing the choice of conditioning sets and even benefits from auto- correlation. The method is order-independent and consistent in the oracle case. A broad range of numerical experiments demonstrates that PCMCI + has higher adjacency detec- tion power and especially more contempo- raneous orientation recall compared to other methods while better controlling false posi- tives. Optimized conditioning sets also lead to much shorter runtimes than the PC algorithm. PCMCI + can be of considerable use in many real world application scenarios where often time resolutions are too coarse to resolve time delays and strong autocorrelation is present