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. The correlation coefficient is now up to 0.88 from 0.77. This is essentially a frequency modulated waveform. The yellow are the areas of discrepancy. This heuristic formula is used to back-extrapolate before 1953.
The quickest way to check how well this will fit the DiffEq of the SOI model is to compare the LHS against the RHS in differential form
$ f''(t) + \omega_0^2 f(t) = Forcing(t) = A*qbo(t) + B*qbo'(t) $
$lhs(t) = rhs(t)$
Check the agreement below. You will see that the majority of the peaks and valleys line up, even before 1953. And they align with an almost hyper-realistic precision. Those that don't are off and that is what causes the correlation coefficient to be kind of low. Remember that this is a differential form so that the noise is amplified !!!
Below the comparison is a power spectra of the residual error. There are some other periodicities in the signal that could be resolved, but otherwise it is pretty flat, closer to white noise.
Again I think that there is something very significant here and all I am trying to do is to get some initial buy-in.
John, thanks for asking me to do a prediction -- but all I am asking is for others to help substantiate this work and perhaps to improve it. Only then would I consider predictions.