[ENH] Auto versions of forecasters

[TonyBagnall]

Describe the feature or idea you want to propose

Its common to have Auto versions of forecasting algorithms that search the hyper parameter space. Our starting design was to have a standard version, e.g. ARIMA and an Auto claa, AutoARIMA, that either contains or extends the standard model. We are continuing in the vein, but since we have got a fair few forecasters in the pipeline, it will result in a lot of class proliferation.

Interested to see what people think

Describe your proposed solution

three options

1. Separate forecasters in separate files, e.g. TAR and AutoTAR in _tar.py and _auto_tar.py
2. Separate forecasters in the same file _tar.py
3. A single forecaster that can be set to perform auto file

I dont really know which I prefer, there are arguments either way, leaning towards (2). The trouble with 3 is it ends up with over parameterised R-like estimators, but it is tidier too.

Describe alternatives you've considered, if relevant

We considered a container for forecaster and optimiser, but the hyper parameter spaces and potential speed ups internally make this not really feasible.

Additional context

No response

[alexbanwell1]

I would suggest 2 makes the most sense as well. A lot of the code is shared between the auto and regular, so it makes sense to have them in the same file. 3 isn't really feasible imo, as different algorithms are best optimised in different ways, and a brute force approach isn't always the best. Worth making sure code is shared as much as possible where relevant, though (as we have done with the Nelder-Mead algorithm).

[TonyBagnall]

ok, lets go with (2) for now unless anyone thinks different