CCM - framework for determining causation

[MKLau]

• coupling determines cross mapping that will be reflected in patterns of correlation (rho ~ Yhat | Mx and Xhat | My)
• differences in convergence on the maximal level of prediction in a time series indicates directionality
• observation error, process noise and times series length influence convergence

transitivity

• X <–> Y <–> Z implies X <–> Z, whether or not X and Z interact directly
• X –> Y, Y –> Z implies X –> Z, whether or not X and Z interact directly
• “Transitivity provides the basis for extending CCM to larger interaction networks, enabling us to distinguish variables that are coupled from those sharing a common driver."

[MKLau]

New R package for CCM from Sugihara's collaborators

https://cran.r-project.org/web/packages/rEDM/vignettes/rEDM_tutorial.html

[MKLau]

Also, the multiSpatialCCM package is designed to work with multiple, "stitched together" time series.

https://cran.r-project.org/web/packages/multispatialCCM/multispatialCCM.pdf

[MKLau]

Distinguishing time-delayed causal interactions using convergent cross mapping

http://www.nature.com/articles/srep14750

Hao Ye, Ethan R. Deyle, Luis J. Gilarranz & George Sugihara Scientific Reports 5, Article number: 14750 (2015) doi:10.1038/srep14750 Download Citation Nonlinear phenomenaPalaeoclimatePopulation dynamics Received: 07 April 2015 Accepted: 18 August 2015 Published online: 05 October 2015

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.