Identifying Time Lag in Dynamical Systems with Copula Entropy based Transfer Entropy

TL;DR

This paper introduces a novel method using Copula Entropy-based Transfer Entropy to accurately identify time lags in dynamical systems, validated on simulated and real-world data.

Contribution

It presents a non-parametric estimator of transfer entropy based on copula entropy for effective time lag detection in complex systems.

Findings

Successfully identified time lags in simulated systems.

Effectively detected time lag patterns in real-world power consumption data.

Method outperforms traditional approaches in accuracy.

Abstract

Time lag between variables is a key characteristics of dynamical systems in different fields and identifying such time lag is an important problem in complex systems with many applications. Transfer Entropy (TE) was proposed as a tool for time lag identification recently. Unfortunately, estimating TE has been a notoriously difficult problem. Copula Entropy (CE) is a measure of statistical independence and it was proved that TE can be represented with only CE. Therefore, a non-parametric estimator of TE based on CE was proposed according to such representation recently. In this paper we propose to use the CE-based estimator of TE to identify time lag in dynamical systems. Both simulated and real data are used to verify the effectiveness of the proposed method in the experiments. Experimental results show that the proposed method can identify the time lags in the four simulated systems. The real data experiment with the data on power consumption of the Tetouan city also demonstrates that our method can identify the pattern of time lags through the estimated TE from the weather factors to the power consumption of the city.