I used the package 'EUREQA', version Formulize, to analyse the monthly smoothed sunspot timeseries from 1750 till 2010.
It gives me a simple formula, with 8 coefficients, that match data with a correlation coefficient of 0.99214404.
In order to obtain a formula only dependent on past values, to ease the projection into some future, I used dS as a one month delayed difference and asked for a formula of the form: S = f(dS, dS^2 , dS^3).
The best formula obtained is:
SunSpots = 27.36486757 + dS + 27.36486757*(sma(dS, 110)) + 21.73018064*(sma(dS, 73)) + 10.03456042*(sma(dS, 34)) + 2.693356275*(sma((dS^2), 131)) + 2.189454695*(sma((dS^2), 403)) + (27.36486757*(sma(dS, 110))*(sma(dS, 110)) - 21.73018064)/(sma((dS^2), 131))
sma(var,length) is the simple moving average.
It reveals a cyclic dependence on 34,73,110,131 and 403 months and a cross between 110 and 131 months (responsable for a long cycle).
The correlation coefficient is quite high, and I expected that the formula could give me some values into the short future. In the last months of the timeseries the error became higher and the formula is quickly divergent in the future.
- What can cause such a discrepancy?
- What kind of physical model could give those components in the formula?
Any ideas ?