A robust time-delay selection criterion applied to convergent cross mapping

This work presents a heuristic for the selection of a time delay based on optimizing the global maximum of mutual information in orthonormal coordinates for embedding a dynamical system. This criterion is demonstrated to be more robust compared to methods that utilize a local minimum, as the global maximum is guaranteed to exist in the proposed coordinate system for any dynamical system. By contrast, methods using local minima can be ill-posed as a local minimum can be difficult to identify in the presence of noise or may simply not exist. The performance of the global maximum and local minimum methods are compared in the context of causality detection using convergent cross mapping using both a noisy Lorenz system and experimental data from an oscillating plasma source. The proposed heuristic for time lag selection is shown to be more consistent in the presence of noise and closer to an optimal uniform time lag selection.