Estimating Conditional Transfer Entropy in Time Series using Mutual Information and Non-linear Prediction

TL;DR

This paper introduces a novel estimator for directed dependencies in time series that improves accuracy over existing methods, especially in complex, highly correlated data, and demonstrates its effectiveness on real EEG data.

Contribution

A new estimator combining non-uniform embedding and greedy selection for better detection of directed dependencies in time series.

Findings

Higher accuracy than existing methods in simulations

Lower false detection rate of instantaneous couplings

Effective application on real EEG data

Abstract

We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new information and improvement of the prediction accuracy provided by the variables. Then, using a greedy approach, the most informative subsets are selected in an iterative way. The algorithm terminates, when the highest ranked variable is not able to significantly improve the accuracy of the prediction as compared to that obtained using the existing selected subsets. In a simulation study, we compare our estimator to existing state-of-the-art methods at different data lengths and directed dependencies strengths. It is demonstrated that the proposed estimator has a significantly higher accuracy than that of existing methods, especially for the difficult case, where the data is highly correlated and coupled. Moreover, we show its false detection of directed dependencies due to instantaneous couplings effect is lower than that of existing measures. We also show applicability of the proposed estimator on real intracranial electroencephalography data.