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

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Document pages: 30 pages

Abstract: Granger causality is a fundamental technique for causal inference in timeseries data, commonly used in the social and biological sciences. Typicaloperationalizations of Granger causality make a strong assumption that everytime point of the effect time series is influenced by a combination of othertime series with a fixed time delay. The assumption of fixed time delay alsoexists in Transfer Entropy, which is considered to be a non-linear version ofGranger causality. However, the assumption of the fixed time delay does nothold in many applications, such as collective behavior, financial markets, andmany natural phenomena. To address this issue, we develop Variable-lag Grangercausality and Variable-lag Transfer Entropy, generalizations of both Grangercausality and Transfer Entropy that relax the assumption of the fixed timedelay and allow causes to influence effects with arbitrary time delays. Inaddition, we propose methods for inferring both variable-lag Granger causalityand Transfer Entropy relations. In our approaches, we utilize an optimalwarping path of Dynamic Time Warping (DTW) to infer variable-lag causalrelations. We demonstrate our approaches on an application for studyingcoordinated collective behavior and other real-world casual-inference datasetsand show that our proposed approaches perform better than several existingmethods in both simulated and real-world datasets. Our approaches can beapplied in any domain of time series analysis. The software of this work isavailable in the R-CRAN package: VLTimeCausality.

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