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

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