This repository contains the implementation of the algortihm for Convergent Cross Mapping (CCM) used in the article:

Mønster, D., Fusaroli, R., Tylén, K., Roepstorff, A., & Sherson, J. F. (2017). Causal inference from noisy time-series data—Testing the Convergent Cross-Mapping algorithm in the presence of noise and external influence. Future Generation Computer Systems, 73, 52-62. DOI: 10.1016/j.future.2016.12.009

In order to use the CCM function xmap() on data from two time series X and Y these have to be phase space embedded, using the time delayed coordinates method. This can be done using the function psembed(). An example of how to use these functions can be seen in the file example.m, which should produce a plot that looks roughly like the figure below. This is the result of CCM on coupled logistic maps with unidirectional coupling. The correlation coefficient between the observed X and the cross-mapped estimates of X (in blue) are observed to converge to high values as the library size L increases, indicating a causal influence of X on Y. The corresponding correlation coefficient between observed Y and cross-mapped estimates of Y are consistently low, and do not display any convergence.

The function psembed returns the phase space embedding MX of a time series X in m dimensions using a time delay tau. The time delay is measured in dimensionless units, i.e., in terms of the vector index.

MX = psembed(X, m, tau);

The function xmap takes as input two time series vectors X and Y and their phase space embeddings MX and MY, the embedding parameters m and tau, the library length L and the sampling method (either 'linear' or 'random') and returns the cross-mapped estimates X_MY and Y_MX along with the corresponding points X1 and Y1 from the original time series.

[ X_MY, Y_MX, X1, Y1] = xmap( X, Y, MX, MY, m, tau, L,'random');

For further details, see the MATLAB implementation source code which is documented, as well as the article. A preprint of an earlier version of the article is also available from arXiv.