[ENH] add ExponentialSmoothing predictor which is able to calculate confidence intervals

Is your feature request related to a problem? Please describe. Sktime does not have exponential smoothing predictor which is able to calculate confidence intervals.

Describe the solution you’d like Include ExponentialSmoothing from statsmodels.statespace in sktime predictors as StateSpaceExponentialSmoothing.

Describe alternatives you’ve considered

Additional context At the moment sktime includes Holt Winter’s exponential smoothing implementation that covers multiplicative trend and seasonal components, but can output pointwise estimations only.

[ltsaprounis]

(Jumping in with some statsmodels detective work)

I had a look at the code and it looks like statsmodels are calculating prediction intervals for state space exponential smoothing models using either the analytical formulas that are based on the the forecast variance (formulas are available for a subset of ETS models) or the simulation technique (i.e. create multiple simulated forecasts by sampling the error terms from the appropriate distribution). This is consistent with the literature (checked Hyndman et al. (2008))

• The function that calculates the forecast variance using the available analytical formulas is _relative_forecast_variance
• The function that calculates the prediction intervals is pred_int (formulas or simulations)

@fkiraly - slightly off-topic but I think adding a simulate method for forecasters that support generating simulated forecasts will be a good feature and we can then have have a single function that generates the prediction intervals using simulations. Example from statsmodels -> simulate

The benefits of using simulations for prediction intervals as well as all the available theoretical formulas for ETS models are in Chapter 6 of Hyndman et al. (2008)

Ref: Hyndman, R. J., Koehler, A. B., Ord, J. K., & Snyder, R. D. (2008). Forecasting with exponential smoothing: The state space approach. Springer-Verlag. http://www.exponentialsmoothing.net

[victordremov]

Thank you for pointing this out. The documentation is definitely calls them confidence intervals, but I guess I’d better check the statsmodels code to be sure.