Causal inference for empirical dynamical systems based on persistent homology

Given two correlated systems, detecting causality between them from observed data is an important but challenging task. Combining two mathematical techniques, delay coordinate embedding and persistent homology, we propose a novel causal inference method for data comprising a pair of scalar time series that are observed from two possibly coupled deterministic dynamical systems. The idea is to encode the topology of the dynamics in the form of the persistent homology of the reconstructed attractors and compare the involved systems by a metric defined on the persistent homology.