Diego D, Haaga KA, Hannisdal B (2018). arXiv:1811.01677
We propose a method for computing the transfer entropy between time series using Ulam’s approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer entropy estimators in that the invariant measure is estimated not directly from the data points but from the invariant distribution of the transfer operator approximated from the data points. For sparse time series, the transfer operator is approximated using a triangulation of the attractor, whereas for data-rich time series we use a faster grid approach. We compare the performance of our method with existing estimators such as the k nearest neighbors method and kernel density estimation method, using coupled instances of well known chaotic systems: coupled logistic maps and coupled Rössler-Lorenz system. We find that our estimator is robust against the presence of moderate levels of dynamical noise. For sparse time series with less than a few hundred observations, our triangulation estimator shows enhanced performance in the presence of dynamical noise. This finding suggests that our method holds some promise for detecting causal directionality between observed time series that are sparse and noisy.
A preprint of the paper is available on arXiv.