Statsmodels: ENH: Add the 4Theta forecasting model

[big-o]

Hello - I've been working as a contributor on the sktime project along with @mloning, which aims to provide a common sklearn-type interface to various time series analysis tools.

A while ago we implemented a basic Theta forecasting model (based on the Hyndman SES + trend approach) and are thinking about implementing the 4Theta variant which amongst other things supports non-linear trends and a multiplicative approach to the modelling.

We saw that you have recently implemented the Optimized Theta Method in statsmodels and wondered if you had any similar plans to implement 4Theta? If so there may be an opportunity to collaborate.

[bashtage]

Contributions in this area are welcome. I added the theta model but have no plans to add any of these extended variants right now.

[big-o]

Thanks - I'll have a chat with the other sktime developers about how we'll be proceeding and keep you updated.

[big-o]

Based on https://github.com/statsmodels/statsmodels/issues/7075#issuecomment-703099140, perhaps it's worth us implementing something in statsmodels and then writing a wrapper for it in sktime? Looking at a paper that @mloning shared with me recently, AutoTheta may be a better implementation choice as it looks more complete than 4Theta:

https://www.researchgate.net/profile/Evangelos_Spiliotis/publication/338507620_Generalizing_the_Theta_method_for_automatic_forecasting/links/5e1dadc5299bf1232603bfd2/Generalizing-the-Theta-method-for-automatic-forecasting.pdf