Papapetrou Maria, Siggiridou Elsa, Kugiumtzis Dimitris
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece.
Entropy (Basel). 2022 Oct 22;24(11):1505. doi: 10.3390/e24111505.
A causality analysis aims at estimating the interactions of the observed variables and subsequently the connectivity structure of the observed dynamical system or stochastic process. The partial mutual information from mixed embedding (PMIME) is found appropriate for the causality analysis of continuous-valued time series, even of high dimension, as it applies a dimension reduction by selecting the most relevant lag variables of all the observed variables to the response, using conditional mutual information (CMI). The presence of lag components of the driving variable in this vector implies a direct causal (driving-response) effect. In this study, the PMIME is appropriately adapted to discrete-valued multivariate time series, called the discrete PMIME (DPMIME). An appropriate estimation of the discrete probability distributions and CMI for discrete variables is implemented in the DPMIME. Further, the asymptotic distribution of the estimated CMI is derived, allowing for a parametric significance test for the CMI in the DPMIME, whereas for the PMIME, there is no parametric test for the CMI and the test is performed using resampling. Monte Carlo simulations are performed using different generating systems of discrete-valued time series. The simulation suggests that the parametric significance test for the CMI in the progressive algorithm of the DPMIME is compared favorably to the corresponding resampling significance test, and the accuracy of the DPMIME in the estimation of direct causality converges with the time-series length to the accuracy of the PMIME. Further, the DPMIME is used to investigate whether the global financial crisis has an effect on the causality network of the financial world market.
因果关系分析旨在估计观测变量之间的相互作用，进而推断观测到的动态系统或随机过程的连通性结构。发现混合嵌入的部分互信息（PMIME）适用于连续值时间序列的因果关系分析，即使是高维序列也适用，因为它通过使用条件互信息（CMI），从所有观测变量中选择与响应最相关的滞后变量来进行降维。该向量中驱动变量滞后成分的存在意味着直接因果（驱动 - 响应）效应。在本研究中，PMIME被适当地应用于离散值多元时间序列，称为离散PMIME（DPMIME）。DPMIME中实现了对离散变量离散概率分布和CMI的适当估计。此外，推导了估计CMI的渐近分布，从而可以对DPMIME中的CMI进行参数显著性检验，而对于PMIME，不存在CMI的参数检验，检验是通过重采样进行的。使用不同的离散值时间序列生成系统进行蒙特卡罗模拟。模拟结果表明，DPMIME渐进算法中CMI的参数显著性检验优于相应的重采样显著性检验，并且DPMIME在直接因果关系估计中的准确性随着时间序列长度的增加收敛到PMIME的准确性。此外，DPMIME被用于研究全球金融危机是否对金融世界市场的因果关系网络有影响。
