[BUG] Internal `coerce_to_period` fails for various dateIndexes about sktime HOT 4 OPEN

I suppose it fails, since pd.date_range(start="2001-01-01", periods=30, freq="M") is resulting in a date time index with ME periodicities. And MEis no supported Period Alias

pd.date_range(start="2001-01-01", periods=30, freq="M")

DatetimeIndex(['2001-01-31', '2001-02-28', '2001-03-31', '2001-04-30',
               '2001-05-31', '2001-06-30', '2001-07-31', '2001-08-31',
               '2001-09-30', '2001-10-31', '2001-11-30', '2001-12-31',
               '2002-01-31', '2002-02-28', '2002-03-31', '2002-04-30',
               '2002-05-31', '2002-06-30', '2002-07-31', '2002-08-31',
               '2002-09-30', '2002-10-31', '2002-11-30', '2002-12-31',
               '2003-01-31', '2003-02-28', '2003-03-31', '2003-04-30',
               '2003-05-31', '2003-06-30'],
              dtype='datetime64[ns]', freq='ME')

(BTW: Using "M" here is also deprecated)

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Additional question in coerce_to_period, we are using the frequency information provided, if one is provided. However, would it be possible to let the frequency just be inferred by pandas?

In that case the error from above would not be raised.

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message hidden, likely AI generated content

The issue you are encountering is related to the limitations of the frequencies supported by pandas PeriodIndex for Periods. Specifically, you mentioned that in pandas 2.2.X, there is a bug where the frequency "2M" is failing to work as expected. It seems that you have observed this issue in pandas 2.2.X, while lower versions are functioning correctly. This issue is relevant to the limitations of period frequencies described in the pandas documentation, specifically the Period Aliases section found at the provided URL.

You mentioned an example code snippet:

ForecastingHorizon([1,2]).to_absolute(pd.date_range("2020", periods=1, freq="2M"))

This code snippet is being impacted by the issue of frequency "2M" not being supported as expected in pandas 2.2.X.

This issue can impact forecasting and time series analysis where the accurate handling of periods and frequencies is crucial.

It's important to note that this issue is related to the specific version of pandas (2.2.X) and the limitations of supported frequencies for Periods.

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Probably duplication of #5131

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