Suggestion: Introduce parameter inverse transformation after fit to rescaled time series

[Kayne88]

Hello,

Excellent work with the library. Has been of great use so far. One thing which required some time to pin down is that parameter estimates are for the rescaled timeseries and not for the original one.

If one wants to calculate analytical quantities based on the parameters or simulate trajectories, they won't resemble the original ones.

It could be an improvement to return the inverse scaled parameter estimates.

For example for a AR(1)+GARCH(1,1) process:
c = c_tilde/C
phi = phi_tilde
omega = omega_tilde/C**2
alpha = alpha_tilde
beta = beta_tilde
where *_tilde denotes the estimates for the scaled process

Cheers

[bashtage]

This is a good idea. I think a slightly better one would be to pass in a scale parameter to the LL which would the rescale the intercept only, which is easy to undo.

[bashtage]

The challenge with descaling is that the effect on the intercept depends on the model, and is non trivial when the model is not linear in the squares, e.g., EGARCH).