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Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method toapproximate the action of the Koopman operator on a linear function spacespanned by a dictionary of functions. The accuracy of EDMD model criticallydepends on the quality of the particular dictionary's span, specifically on howclose it is to being invariant under the Koopman operator. Motivated by theobservation that the residual error of EDMD, typically used for dictionarylearning, does not encode the quality of the function space and is sensitive tothe choice of basis, we introduce the novel concept of consistency index. Weshow that this measure, based on using EDMD forward and backward in time,enjoys a number of desirable qualities that make it suitable for data-drivenmodeling of dynamical systems: it measures the quality of the function space,it is invariant under the choice of basis, can be computed in closed form fromthe data, and provides a tight upper-bound for the relative root mean squareerror of all function predictions on the entire span of the dictionary.

Temporal Forward-Backward Consistency, Not Residual Error, Measures the Prediction Accuracy of Extended Dynamic Mode Decomposition