I'm not an expert in this but I'm suspicious of
polynomial curve fitting.
In both of these cases we have assumed a global \ (\ phi \) parameter, and found it by
polynomial curve fitting of mean vs variance.
Not exact matches
With your mouse, drag data points and their error bars, and watch the best -
fit polynomial curve update instantly.
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.
However, although its simple linear regression analysis facilities (including
polynomials) provides automatically the option for plotting the
fit with CIs for the
fitted line /
curve and for future observations from the same population, I am unsure about these intervals for autocorrelated data — typically time series.
The dark black, grey and bright red
curves are second order
polynomial fitted trends produced by Excel - they are not predictions, but they do indicate the current direction the trends are taking.
Attributing climate is more like figuring out the structure of DNA than it is like figuring out the laws of quantum mechanics — simple
curve -
fitting («exponentials,
polynomials») doesn't cut it.
By analogy with certain sets of data that are actually generated by say a quadratic function or other
polynomial, there might be sections where the
curve is almost flat and happens to match a linear
fit, but that linear
fit will then diverge from the more complicated reality.
Has anyone tried to do an nth order
polynomial or a Fourier series
curve fit on the climate data?
Least squared
curve fit to an N - th order
polynomial?