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Overview: convergent cross mapping (CCM)

The convergent cross mapping (CCM) algorithm 1 measures how well a delay embedding of a putative response time series is able to predict a putative driver time series. The prediction skill is then taken as the unidirectional coupling strength from the driver to the response time series. One may also compute lagged CCM 2 by tuning the ν parameter.

The following cross mapping estimators are implemented.

  • crossmap. Cross map for time series of fixed length. This algorithm can implicitly say something about convergence by adjusting the library size.
  • convergentcrossmap. Explicitly cross map over multiple time series lengths. This is the approach introduced in 1.

Example

In the animation below, we're cross mapping for increasing time series length for a undirectionally set of coupled Henon maps where x drives y. As expected from the underlying coupling, the cross mapping skill in the direction x → y converges at a higher value than in the opposite direction.

  • CauseMap.jl also provides an implementation of the CCM algorithm, but this package has not been updated since 2015.

  1. Sugihara, G., May, R., Ye, H., Hsieh, C. H., Deyle, E., Fogarty, M., & Munch, S. (2012). Detecting causality in complex ecosystems. Science. https://doi.org/10.1126/science.1227079 ↩↩

  2. Ye, H., Deyle, E. R., Gilarranz, L. J., & Sugihara, G. (2015). Distinguishing time-delayed causal interactions using convergent cross mapping. Scientific Reports. https://doi.org/10.1038/srep14750 ↩