> Since Graham evidently thought that my QBO model was not good enough, I let Eureqa generate a much better cross-validated time series from the data available.

Oh dear. You have completely missed the point I have been trying to make. I don't know whether this is because you have no interest in doing what I think you need to do, or because you lack the background to understand. Your comment to John "Only then would I consider predictions" makes me think its the former. Your mentioning that Eureqa uses cross-validation makes me think its the latter.

This is my main point:

> I haven't seen you actually demonstrate your ability to extraprolate the QBO. Its obvious from your graph this is possible to some extent, but how much? If you feed half of the data (1953-1983 say) into FindFormula and then extrapolate to 2013, how accurately can you do this? I would want to do lots of tests like this before extrapolating into the unknown.

Cross-validation is just a more systematic way (or set of ways) of doing this. It involves dividing up the available to data to make best use (we hope) of a small amount of data for some purpose. A very common purpose is to assess the ability of a method to extrapolate. The basic idea is already contained in the paragraph I just quoted. The fact that Eureqa uses cross-validation internally is irrelevant. The point is to test the model produced by Eureqa on data that Eureqa has never seen.