API: Change Period('NAT') to return NaT, not Period instance

[sinhrks]

Code Sample, a copy-pastable example if possible

Timedelta returns NaT when input can be regarded as NaT. Otherwise Period returns its special representation (This was done in #7485 prior to Timedelta).

pd.Timedelta('NaT')
# NaT

pd.Period('NaT', freq='M')
# Period('NaT', 'M')

Expected Output

pd.Period('NaT', freq='M')
# NaT

The fix should affects:

• Period and PeriodIndex, Series ops
  • add, sub, comp
• PeriodIndex creation from list-like which contains Period and NaT (ENH: PeriodIndex now accepts pd.NaT #13430)
• PeriodIndex boxing
• .to_period
• __contains__ any NaT-like(pd.NaT, None, float('nan'), np.nan) (Checking for NaT in PeriodIndex doesn't work with None, pd.NaT #13582)

output of pd.show_versions()

Current master.

[jreback]

yep, looks good.