[ENH] STL and MSTL transformer

[TinaJin0228]

Reference Issues/PRs

#2851

What does this implement/fix? Explain your changes.

This implements the STL (Seasonal-Trend decomposition using Loess) transformer, which is a filtering procedure for decomposing a seasonal time series into three components: trend, seasonal, and remainder.

Does your contribution introduce a new dependency? If yes, which one?

No.

Any other comments?

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[TinaJin0228]

MSTL (#2849 )is also implemented in the same feature branch, as it is closely related to STL.

[TinaJin0228]

I compared the decomposition performance of Aeon's mstl transformer and R::forecast's mstl() with a simulated data sample, following the approach described in Sections 3.2 and 3.3 of the paper. Here is the record:

=== RMSE summary over replications ===
Periods: [24, 168], iterate=2, s_windows=R/aeon defaults, n=672, reps=10, sigma=0.2, slope=0.01

AEON (MSTL):
         S24:  mean=  0.083433  median=  0.084952
        S168:  mean=  0.127435  median=  0.128592
       S_sum:  mean=  0.150322  median=  0.150577
       Trend:  mean=  0.015426  median=  0.013789
   Remainder:  mean=  0.150891  median=  0.151237

R (forecast::mstl):
         S24:  mean=  0.073217  median=  0.073347
        S168:  mean=  0.114912  median=  0.114949
       S_sum:  mean=  0.133834  median=  0.133319
       Trend:  mean=  0.030561  median=  0.029889
   Remainder:  mean=  0.130836  median=  0.131252

AEON / R  (mean RMSE ratios; <1 favors AEON, ~1 is parity)
         S24:      1.1395
        S168:      1.1090
       S_sum:      1.1232
       Trend:      0.5048
   Remainder:      1.1533

[TinaJin0228]

I accelerated the stl (and mstl) transformer and it is now much faster than that of statsmodel and statsforecast: