Reliable detection of causal asymmetries in dynamical systems.

Knowledge about existence, strength, and dominant direction of causal influences is of paramount importance for understanding complex systems. Current methods deduce ambiguous causal links among different observables from (complex) dynamical systems, if a limited amount of realistic data is used. It is particularly difficult to infer the dominant direction of causal influence for synchronizing systems. Missing is a statistically well defined approach that avoids false positive detection while being sensitive for weak interactions. The proposed method exploits the local inflation of manifolds to estimate upper bounds on the information loss among state reconstructions and tests for the absence of causal influences. Simulated data demonstrates that it is robust to intrinsic noise, copes with synchronization, and tolerates moderate amounts of measurement noise.