If a net accurately models all of the salient deterministic characteristics of an input-output relationship, the error will not be significantly correlated with the input and the cross-correlation function will be indistinguishable from that of the input and random noise.
If a net accurately models all of the salient predictive characteristics of a time series lag relationship, the error will not be significantly autocorrelated and the auto-correlation function will be indistinguishable from that of random noise.
Thank you for formally accepting my answer.
Greg
