[DOC] ExponentialSmoothing default method change from L-BFGS-B to SLSQP

[manuel-munoz-aguirre]

Reference Issues/PRs

While exploring #6175, realized that the default parameter for method in Exponential Smoothing should be SLSQP. This also affects statsmodels documentation and there is already an open PR in their repo to fix this.

What does this implement/fix? Explain your changes.

Changes method='L-BFGS-B' to method='SLSQP'.

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

No

What should a reviewer concentrate their feedback on?

See statsmodels default

Did you add any tests for the change?

N/A

Any other comments?

N/A

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[fkiraly]

Thanks!

Quick question, may I clarify which of the following is the case:

• None translates to SLSQP in statsmodels already
• None will translate to SLSQP in statsmodels at some future point, when a planned PR is going to be merged and the default will change
  • this, and statsmodels is not raising a deprecation warning
  • this, and statsmodels is, or will be raising a depercation warning

Depending on what is the case here, we may have to take additional steps, in accordance with change/deprecation policy:
https://www.sktime.net/en/latest/developer_guide/deprecation.html

As a first step, I feel we should change the default from None to what it currently is in statsmodels. FYI @benHeid, @yarnabrina

[yarnabrina]

@fkiraly based on the shared link above, it seems statsmodels uses SLSQP already when method is specified as None, and the Git blame is 4 years old. We may not need deprecation cycle as no behaviour will change, and this PR can be considered just as a docs update.

https://github.com/statsmodels/statsmodels/blame/192670b31c9069b247b0901d66013853e2ca47b7/statsmodels/tsa/holtwinters/model.py#L1142

[fkiraly]

Makes sense.

In that case, we should consider changing the sktime default to "SLSQP" (separate from this PR), to avoid behaviour switching again.

[manuel-munoz-aguirre]

Should I go ahead and open a new PR switching the default value from None to SLSQP? @fkiraly

[fkiraly]

Not sure whether we should. Since it is a very small change, how about this - you open a PR, and then we discuss with other core devs what they think?