Variable-lag Granger Causality and Transfer Entropy for Time Series Analysis

TL;DR

This paper introduces variable-lag Granger causality and Transfer Entropy methods that relax fixed delay assumptions, improving causal inference in complex time series like financial markets and collective behavior.

Contribution

It develops novel variable-lag causality measures using Dynamic Time Warping, enabling more accurate causal inference in diverse real-world applications.

Findings

Outperforms existing methods in simulated datasets

Effective in analyzing collective behavior

Applicable across various domains

Abstract

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop Variable-lag Granger causality and Variable-lag Transfer Entropy, generalizations of both Granger causality and Transfer Entropy that relax the assumption of the fixed time delay and allow causes to influence effects with arbitrary time delays. In addition, we propose methods for inferring both variable-lag Granger causality and Transfer Entropy relations. In our approaches, we utilize an optimal warping path of Dynamic Time Warping (DTW) to infer variable-lag causal relations. We demonstrate our approaches on an application for studying coordinated collective behavior and other real-world casual-inference datasets and show that our proposed approaches perform better than several existing methods in both simulated and real-world datasets. Our approaches can be applied in any domain of time series analysis. The software of this work is available in the R-CRAN package: VLTimeCausality.