Abstract
An important problem across many scientific fields is the identification of causal effects from observational data alone. Recent methods (convergent cross mapping, CCM) have made substantial progress on this problem by applying the idea of nonlinear attractor reconstruction to time series data. Here, we expand upon the technique of CCM by explicitly considering time lags. Applying this extended method to representative examples (model simulations, a laboratory predator-prey experiment, temperature and greenhouse gas reconstructions from the Vostok ice core, and long-term ecological time series collected in the Southern California Bight), we demonstrate the ability to identify different time-delayed interactions, distinguish between synchrony induced by strong unidirectional-forcing and true bidirectional causality, and resolve transitive causal chains.
Highlights
CCM can be successfully applied to systems with weak to moderate coupling strengths, Sugihara et al observed that exceptionally strong unidirectional forcing can lead to the phenomenon of “generalized synchrony”[7]
In the case of synchrony caused by strong unidirectional forcing, this approach should detect a negative lag for cross mapping in the true causal direction and a positive lag in the other direction
As shown in the first panel (Fig. 1A), where causation occurs with an effective delay of 1 time step (y(t) affects x(t + 1 ) and vice-versa), the optimal cross mapping in both directions occurs at a lag of − 1
Summary
CCM can be successfully applied to systems with weak to moderate coupling strengths, Sugihara et al observed that exceptionally strong unidirectional forcing can lead to the phenomenon of “generalized synchrony”[7]. As shown in the first panel (Fig. 1A), where causation occurs with an effective delay of 1 time step (y(t) affects x(t + 1 ) and vice-versa), the optimal cross mapping in both directions occurs at a lag of − 1. Extending this analysis to systems with random coefficients (see Supplementary Information), the result is robust, with only a few outliers that exhibit optimal cross mapping at different lags (Figure S1).
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