Have to thank Graham for putting up this topic of QBO predictability.

I was going through some old Eureqa machine leaning experiments on QBO and once again realized the significance of what it found.

Started with raw QBO data


Next targeted a solution with sinusoidal factors
maximizing correlation coefficient


Then let Eureqa crank away for 20 hours


Picked a high complexity solution
(high complexity doesn't matter as the other solutions have similar components)


The two strongest factors that Eureqa found
which were sinusoids with an obviously folded or aliased frequency

strength aliased freq period days actual % error
78 2.66341033 2.359075219 27.20894362 27.212=draconic 0.011233004
35 2.29753386 2.734751989 29.53743558 29.531=synodic -0.021787874

The two factors have periods when unaliased that match the draconic and synodic lunar month, with errors 0.01% and 0.02% respecively

What are the chances of that?