双变量时间序列数据的因果关系指数：性能比较综述
Causality indices for bivariate time series data: a comparative review of performance
摘要：
多变量纵向数据之间的非线性和非对称因果关系的推断是一项具有挑战性的任务，具有广泛的应用领域，包括临床医学，数学生物学，经济学和环境研究。在复杂动态和随机系统中，因果关系的推断方法很多，但至今还没有一个统一一致的因果关系定义。我们评估了10个突出的双变量因果关系指数的时间序列数据的性能，在四个模拟模型系统，具有不同的耦合方案和特点。在进一步的实验中，我们表明，这些方法可能并不总是不变的真实世界的相关转换（数据的可用性，标准化和缩放，舍入误差，缺失数据和噪声数据）。我们建议转移熵和非线性格兰杰因果关系可能是特别强大的指标，估计在现实世界中的应用二元因果关系。最后，我们提供了灵活的开放访问Python代码，用于计算这些方法和模型模拟。
英文摘要：
Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed but there is not a unified consistent definition of causality in this context. We evaluate the performance of ten prominent bivariate causality indices for time series data, across four simulated model systems that have different coupling schemes and characteristics. In further experiments, we show that these methods may not always be invariant to real-world relevant transformations (data availability, standardisation and scaling, rounding error, missing data and noisy data). We recommend transfer entropy and nonlinear Granger causality as likely to be particularly robust indices for estimating bivariate causal relationships in real-world applications. Finally, we provide flexible open-access Python code for computation of these methods and for the model simulations.
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