An improved approach to convergent cross mapping method for strongly coupled time series data

In numerous scientific domains, a significant challenge lies in identifying causal relationships among the various components of a system solely based on observational data. Recently, the convergent cross mapping (namely, CCM) method proposed by Sugihara et al. has demonstrated substantial potential for causal inference in the absence of models. By varying the coupling strength of the coupled Logistic model, we found that for asymmetrically strongly coupled time series, the CCM method fails in inferring both the direction and strength of causal relationships. In this paper, we propose an improved version of the CCM method, termed effective mutual information convergent cross mapping (namely, EMICCM) method, by considering inherent characteristics of time series such as nonlinearity and non-normal distribution features. As most real systems exhibit nonlinear and non-normally distributed characteristics, our method offers a more accurate measure for inferring causal relationships within them.