Here's another way of looking at it: A coin flip would have given a 50% chance of heads in any given month, so the probability was 1/2 for each month. The probability of its coming up heads two months in a row is 1/2 x 1/2 = (1/2)^2, i.e., one-half squared. The probability of its coming up heads 108 months in a row would be (1/2)^108 = 3.08 x 10^-33. The probability of it then coming up tails in the next month was 1/2, so the chance of the model staying favorable for 108 months by random chance and then switching to favorable was the product, or 3.08 x 10^-33 x 1/2 = 1.54 x 10^-33.
The probability of its staying unfavorable for the following 38 months (I already counted the first of the 39 months in the preceding paragraph) is (1/2)^38 = 3.6 x 10^-12. Then there is a 50% chance of it switching to favorable the next month, for a total probability of 3.6 x 10^-12 x 1/2 = 1.8 x 10^-12.
The combined probability for both periods is again the product, or 1.54 x 10^-33 x 1.8 x 10^-12 = 2.77 x 10^-45. Thus, the probability that the model would have stayed favorable for nine years, gone unfavorable for three years, and then gone favorable again, all by random chance, is exceedingly small.
Fascinating.
