Let's remove the very - long - term trend by subtracting
a cubic polynomial fit, leaving this:
Not exact matches
Simple
fit to the 1975 - 2012 HADCRUT monthly data with quadratic and
cubic polynomials gives significantly better R ^ 2 over the whole range.
At the moment a
cubic polynomial is the best
fit to the mean temperature but in future this may not be the case.
In the figure the continuous brown curve is an estimate by locally weighted regression (loess)-- using a locally -
fitting cubic polynomial and the standard «tri-cube» weighting.
But this time a
cubic (3rd - degree)
polynomial fit is significant.
It looks to be a
polynomial fit, and least a
cubic and possibly a higher order.
It's like they are claiming a great coup for
fitting 4 points to a
cubic polynomial.