I'm afraid that I was always taught that curve fitting is good (with
caveats) for interpolation but to be avoided as far as humanly possible
for extrapolation.

(Because there is always a serious danger that a model that appears to
be a good fit over a limited range of data can become - potentially -
absurdly wrong the further the curve is pushed beyond the available
data. This is especially so if the model equation includes some sort of
power function and/or is not grounded in some credible physical hypothesis.)

This obviously presents a real difficulty for forecasts of climate
change and related parameters where - short of becoming time travellers
- there is no choice but to try to extrapolate into the future. But it
needs to be done with real caution if the parameter values are to be at
all useful or credible, whatever the nominal SSR might suggest.