ScoreΒΆ
The way the predictions are evaluated in the paper is by using the coefficient of determination between the predictions and the actual value. This is done for all the predictions at multiple library lengths. If the predictions for \(X_1\) are better than \(X_2\) than it is said that \(X_1\) influences \(X_2\).
In the plot above, the blue line has a higher forecast skill than the green line. This indicates that the blue system is forcing the green system. Another important feature is that they converge as the library length is increased. This indicates that the shadow manifold has been appropriately populated and novel predictions can be made.