I took a casual look at commenter Mr. Dan Pangburn's analysis of climate and sunspots. He has an expression, I think his "time integral" of sunspots as follows. Sum over years the difference between the number of sunspots for that year and the average number of sunspots per year times the fourth power of the ratio of the temperature for that year and the average temperature. Throw in a multiplicative and additive fudge factor and you have his model. The most obvious problem with this model is that it includes the very temperature that he is trying to model in the model. Now it might take some mathematical slight of hand to get temperature out of there, but if you already put it in it sure shouldn't be surprising. For each year you are subtracting the average number of sunspots times a number close to 1 from the number of sunspots.