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

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  • Chainarong Amornbunchornvej
  • Elena Zheleva
  • Tanya Berger-Wolf

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.

Suggested Citation

  • Chainarong Amornbunchornvej & Elena Zheleva & Tanya Berger-Wolf, 2020. "Variable-lag Granger Causality and Transfer Entropy for Time Series Analysis," Papers 2002.00208, arXiv.org, revised Jun 2020.
  • Handle: RePEc:arx:papers:2002.00208
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    References listed on IDEAS

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    1. Erdal Atukeren, 2010. "The relationship between the F-test and the Schwarz criterion: Implications for Granger-causality tests," Economics Bulletin, AccessEcon, vol. 30(1), pages 494-499.
    2. repec:ebl:ecbull:v:30:y:2010:i:1:p:494-499 is not listed on IDEAS
    3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    4. Chainarong Amornbunchornvej & Elena Zheleva & Tanya Y. Berger-Wolf, 2019. "Variable-lag Granger Causality for Time Series Analysis," Papers 1912.10829, arXiv.org.
    5. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
    6. Giorgino, Toni, 2009. "Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i07).
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