Abstract: The convergent cross mapping (CCM) is a method to analyze causality of nonlinear time series variables. Different from the traditional linear system analysis method, CCM gets historical information based on their state space reconstruction. The presence of causality can be confirmed when the estimated values perform convergent with time series extension. Here, we introduced the develop-ment history of CCM and its advantages over the traditional Granger causality test, and elaborated the principle, algorithm process, and implementation approach. As a system analysis method aiming at the coupling relationship between variables from weak to moderate, CCM can effectively solve the complex causality among nonlinear multivariable in ecosystems. When it is applied to the causality analysis of multi-point time series variables with spatial information, the spatial autocorrelation among points should be fully considered and combined with the method that can remove the spatial correlation between variables and sequences, so as to ensure more accurate causality analysis using CCM and more convincing results.

Key words: convergent cross mapping (CCM), causality, Granger causality test, nonlinear complex ecosystem