Theta forecaster and prediction intervals

[big-o]

Reference Issues/PRs

#67 #97

What does this implement/fix? Explain your changes.

Includes:

• ThetaForecaster which implements the Theta method.
• Unit tests for ThetaForecaster.
• A new dataset in datasets.load_airline - the Box/Jenkins airline passengers dataset. I thought this provided a clearer example of simple, univariate, seasonal data than some of the other datasets currently in sktime.
• New interface in BaseForecaster to enable prediction intervals to be calculated: prediction_errors. Currently this has only been implemented for ThetaForecaster. Running this method for any other forecaster will raise a NotImplementedError.
• Alternatively, prediction intervals may also be obtained by calling predict() and providing one or many confidence levels. This will cause the method to return a tuple of predictions and errors, instead of just predictions.
• A plot() convenience method for forecasters. As well as plotting the forecasts (optionally alongside any training/test data), it will also plot prediction intervals if available for that forecaster.
• A new notebook, simple_forecasting.ipynb, to demonstrate all of the above.

Any other comments?

Other projects I looked at like as pmdarima and R's forecast library return upper and lower bounds for prediction intervals. I've opted for a different approach though, of just doing the bare minimum and calculating the forecast point errors and returning this as a single series. It's then trivial to apply this to your forecasts to obtain the intervals. This is what the new plot() method does under the hood. I think it should still be fairly easy to interface with some of these other packages even with this different approach but please let me know if you disagree.

FYI, prediction_errors supports the calculation of producing PIs at different confidence levels, something that was discussed in #97. It also allows each forecaster to define its own methods for PI calculations. I didn't attempt to implement this for any of the other forecasters as this could be quite a lot of code for some of them (in the case of ETS forecasting, I believe some models don't even have a known formula - for this reason I implemented the interface in a way that makes it optional).

I thought about merging in the new notebook with the existing forecasting notebook, but wasn't sure how to best make them fit together. I'm happy to take a steer on this if you'd prefer me to put all the forecasting stuff in a single notebook before merging the PR.

PR checklist

• I have added unit tests and made sure they pass locally.
• I have updated the existing example notebooks or provided a new one to showcase how my algorithm works.
• I have updated sktime's estimator overview and I'm committed to maintain my contribution and provide bug fixes if necessary.

[mloning]

Great work! I've added a few minor comments!

[mloning]

Nice, great work!