Leonidas Tsaprounis

The naive methods' forecast variance can be expressed analytically under the 2 assumptions below: - forecast values are normally distributed - residuals are uncorrelated https://otexts.com/fpp3/prediction-intervals.html#benchmark-methods

Have you tried using it as the regression in `make_reduction` ? If it's scikit-learn compatible, it should work.

`predict_proba_sample` sounds like we're sampling from the distribution of each time step as if they where independent. It's usually a recursive sampling from the 1-step ahead forecast distribution (unless we...

> Also, how are we going to handle the various parameters that are specific to the simulation interfaces? We'll treat it in the same way as `predict` and `predict_quantiles`! For...

One more point from me: - Use of transformers that are applied on the index such as the `DateTimeFeatures` transformer and other transformers that could be applied to the hierarchy...

> * use of contemporary `X`, use of shifted `X` (by forecasting horizon) Would that force passing `fh` on fit?

> These changes are great. I was wondering: what about the use of covariates in X of which we do not know the future values? I think the clean solution...

Also we need a way to create exogenous variables based on the absolute horizon. For example, dummy seasonality ([DateTimeFeatures](https://github.com/alan-turing-institute/sktime/blob/0bd87682f0b67ff2fec49921a43d2fc17674205a/sktime/transformations/series/date.py)) and/or Fourier features (coming soon) are exogenous variables of the form...

@DBCerigo - FYI sktime template pattern motivation / explanation https://github.com/sktime/sktime-workshop-pydata-london-2022/blob/main/notebooks/2_basic_extensions.ipynb

@srggrs - the code quality checks are failing. These are usually simple formatting rules (e.g. a line should not exceed 88 characters in length). To avoid any surprises from this,...