Derived feature request from discussion wiht @ggjx22 in #6279.

The request is to implement the Syntetos/Boylan expert classification of time series, from Syntetos/Boylan (2005), The accuracy of
intermittent demand estimates, IJF.

Good first issue, should be simple to implement, so no need to interface from anywhere - recipe is here: https://www.sktime.net/en/latest/developer_guide/add_estimators.html

I would specify the estimator as follows:

Type

Series-to-primitives transformer. Per-instance.

Parameters

• optional parameters "adi_threshold", "cv_threshold", default values are 1.32, 0.49, as in the paper.
• optional parameter features, by default all parameters are computed. If not None, List of str, must contain "adi", "cv2", "class".

Behaviour

Computes three features or a subset thereof, as columns of the return of transform:

• adi - average demand interval. This is the same as last index minus first index, divided by number of non-zero values minus one. For time like indinces, the unit should be in number of periods. Not sure what to do for non-periodic - if freq is unavailable, I would just drop the index.
  • there are some random references on the internet, which give adi as simply the fraction of non-zero values. Afaik that is not accurate in comparison to the original reference, the "minus one" does not cancel.
• cv2 - this is just variance/(mean squared), but taken on the sample of values that are non-zero, in the series. The reference uses the biased estimator for variance, i.e., divide by number of values (not minus one)
• class - derived class, string column, depending on whether adi <= adi_threshold and cv <= cv_threshold. Yes/yes is called "smooth", yes/no "erratic", no/yes "intermittent", no/no "lumpy", by the authors.