Especially, most of these methods work not well in nonlinear systems due to the high false-positive rate, which is the proportion of all cases without causal links but incorrectly detected to be casually linked.
![false causality false causality](https://images.slideplayer.com/35/10318787/slides/slide_8.jpg)
These methods were compared in previous study in which they found that different causality detection methods perform differently to linear or nonlinear systems. Many causality detection and quantification methods have been developed, among them six frequently used methods are Granger causality (G) test and its extended Granger causality test (EG) kernel Granger causality test (KG), transfer entropy (TE), convergent cross mapping (CCM) and predictability improvement (PI).
![false causality false causality](https://i0.wp.com/khaboreprakash.com/wp-content/uploads/2021/11/Would-you-be-able-to-render-services-in-case-of.jpg)
Causality detection and quantification can make up for these deficiencies found in correlation metrics. However, interactions are mostly direction-dependent, and correlation metrics usually cannot provide information related to interaction direction. Correlation metrics, such as Pearson's correlation coefficient, Spearman's rank correlation coefficient, Kendall's tau coefficient and so on have been widely adopted to reach these goals.
#FALSE CAUSALITY SERIES#
Interactions between two variables or associations between two processes or two measured series are important issues in wide fields. Three typical coupled systems with known causal links are applied to show the better performance of new Reservoir Computing Granger (RCG) method over traditional nonlinear Granger causality and its extension methods, which indicates that RCG can accurately detect causal relationships in complex systems and its great potential in exploring the causal and interaction relationships from observational time series. In this study, a new method combining the advantages of Reservoir Computing (RC, a machine learning method) and classical Granger causality detection was developed to fully solve false-positive problems or considerably lower the false-positive rate in detecting causal links of nonlinear systems. Compared to false-negative problem, false-positive is a more serious problem found in nonlinear systems or processes for almost all causality detection methods.
![false causality false causality](https://wronghands1.files.wordpress.com/2017/03/working-causality-loop.jpg)
However, most of them often suffer from the false detection problems, including false-positive (detected causal links do not exist) and false-negative (an existing causal link fails to be detected). Many methods have been developed to detect and identify the possible causal link between two variables. Identifying causal and interaction relationships from observational time series is a key step toward understanding complex systems and is also a challenging problem.