Design and implementation of ColumnEnsembleForecaster

References re-design of Theta Forecaster #854 Implements ThetaLinesTransformer #923

Describe the solution you’d like Implement ColumnEnsemble multivariate to univariate forecaster. It forecasts transformed data (pd.Dataframe returned by ThetaLinesTransformer) with Theta model’s standard case where theta_coefficient = [0, 2]. Should return pd.Series - the average of the two forecasts (linear regression and SES with drift).

Related issues: Poor Theta model predictions #421 Implementation of AutoTheta Forecaster #738

Existing implementations:

• in sktime sktime/forecasting/theta.py (theta parameter is assumed)

other implementations in R:

• Theta https://rdrr.io/cran/forecast/man/thetaf.html
• AutoTheta https://github.com/vangspiliot/AutoTheta/blob/master/code
• M4 AutoTheta https://github.com/Mcompetitions/M4-methods/tree/master/260 - KaterinaKou
• 4Theta https://github.com/Mcompetitions/M4-methods/blob/master/4Theta method.R
• (boxcox + theta) https://github.com/Mcompetitions/M4-methods/blob/master/260 - KaterinaKou/final_M4.R
• Theta in statsmodels https://www.statsmodels.org/devel/examples/notebooks/generated/theta-model.html
• differencing is implemented in https://alkaline-ml.com/pmdarima/_modules/pmdarima/utils/array.html#diff

[Lovkush-A]

Happy I could help!

Note that if modular aggregator does not work, it might still be a good idea to have a multivariate-to-multivariate ensemble forecaster.

[fkiraly]

@GuzalBulatova, I do like this idea.

One point I wanted to bring up is the handling of input and output types - the ColumnEnsembleForecaster takes a multivariate series and produces a univariate one. The theta transformer takes a univariate and produces a multivariate. I don’t think we have agreed on conventions.

Also, you allude to the initial conversion series->frame being done in the base class.

My thought would be that after #980 this would be automatically taken care of (and input/output types do not matter in the implementation), but in any case we need to think carefully about the conversions and the types involved. There seem to be a lot of case distinctions if we want to have the logic in _fit.