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

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 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.

Exploring the Effect of Climate Risk on Agricultural and Food Stock Prices Fresh Evidence from Emd-Based Variable-Lag Transfer Entropy Analysis

“…Typically, we infer whether 𝑋 causes 𝑌 by computing the transfer entropy ratio 𝑇 (𝑋, 𝑌 ) = 𝑇 𝑋→𝑌 ∕𝑇 𝑌 →𝑋 , if 𝑇 (𝑋, 𝑌 ) > 1 then we state that 𝑋 causes 𝑌 . However, Amornbunchornvej et al (2020) proves that the Granger causality test is limited by the fixed-lag assumption, then, to overcome this problem, the authors propose a variable-lag Granger causality test (Amornbunchornvej et al, 2020). In addition, since transfer entropy is a nonlinear extension of Granger causality test, Amornbunchornvej et al (2021) show that transfer entropy is also limited by the fixed-lag assumption.…”

“…, 𝑃 is the alignment sequence between 𝑋 and 𝑌 (see definition 5.1 in Amornbunchornvej et al, 2021) and 𝛥 𝑡 ∈ 𝑃 where 𝛥 𝑡 > 0. Based on Eqs.…”

“…The procedure for the variable-lag transfer entropy causality test is as follows: given two time series 𝑋 and 𝑌 , first, using the Dynamic Time Warping (DTW) method (Amornbunchornvej et al, 2020(Amornbunchornvej et al, , 2021, the time series 𝑋 DTW is reconstructed based on 𝑋 which is most similar to 𝑌 . DTW calculates the distance between two time series by aligning sufficiently similar patterns between them, while allowing for local stretching.…”

“…EMD is more suited for decomposing nonlinear and nonstationary time series than other decomposition methods, such as wavelet and the Fourier decomposition method (Chang et al, 2021). In addition, we apply the VL transfer entropy approach proposed by Amornbunchornvej et al (2021) that can infer a causal relation of Granger or transfer entropy where a cause impacts an effect with arbitrary delays that can change dynamically, and also to report the similarity of time series patterns between the cause and the delayed effect, for arbitrary delays. Moreover, our research is also connected to the body of literature that examines the consequences of natural disasters (Berkman et al, 2011;Tsai and Wachter, 2015;Huang et al, 2018;Keleş et al, 2018;Chang and Jennifer, 2022;Chen et al, 2022).…”

Framework for inferring empirical causal graphs from binary data to support multidimensional poverty analysis

“…Causal inference plays a key role for explanation, prediction, decision making, etc. [10,24]. It reveals causal relations between variables/factors, which leads to the understanding of influence among variables.…”