BUG: inconsistency in freq of DatetimeIndex when converting PeriodIndex.to_timestamp

[natmokval]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd
per = pd.PeriodIndex(['2012-01', '2012-04', '2012-07'], dtype='period[Q]') 
per.to_timestamp(how='start')

per = pd.PeriodIndex(['2012-01', '2012-04'], dtype='period[Q]') 
per.to_timestamp(how='start')

per = pd.PeriodIndex(['2012-01', '2012-02', '2012-03'], dtype='period[M]') 
per.to_timestamp(how='start')

per = pd.PeriodIndex(['2012-01', '2012-02'], dtype='period[M]') 
per.to_timestamp(how='start')

Issue Description

this outputs

per = pd.PeriodIndex(['2012-01', '2012-04', '2012-07'], dtype='period[Q]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-04-01', '2012-07-01'], dtype='datetime64[ns]', freq='QS-OCT')

per = pd.PeriodIndex(['2012-01', '2012-04'], dtype='period[Q]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-04-01'], dtype='datetime64[ns]', freq=None)

per = pd.PeriodIndex(['2012-01', '2012-02', '2012-03'], dtype='period[M]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-02-01', '2012-03-01'], dtype='datetime64[ns]', freq='MS')

per = pd.PeriodIndex(['2012-01', '2012-02'], dtype='period[M]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-02-01'], dtype='datetime64[ns]', freq=None)

Expected Behavior

during conversion PeriodIndex.to_timestamp freq in DatetimeIndex unexpectedly depends on len of data. Shouldn't freqs in all examples above be equal 'QS-OCT' and 'MS', but not None?

per = pd.PeriodIndex(['2012-01', '2012-04'], dtype='period[Q]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-04-01'], dtype='datetime64[ns]', freq='QS-OCT')

per = pd.PeriodIndex(['2012-01', '2012-02'], dtype='period[M]')
per.to_timestamp(how='start')
DatetimeIndex(['2012-01-01', '2012-02-01'], dtype='datetime64[ns]', freq='MS')

Installed Versions

INSTALLED VERSIONS

commit : b7a2207
python : 3.10.13.final.0
python-bits : 64
OS : Linux
OS-release : 4.19.0-22-amd64
Version : #1 SMP Debian 4.19.260-1 (2022-09-29)
machine : x86_64
processor :
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 2.1.0.dev0+1330.gb7a220731e.dirty
numpy : 1.26.0
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.1.2
pip : 23.3.1
Cython : 3.0.5
pytest : 7.4.3
hypothesis : 6.89.0
sphinx : 7.2.6
blosc : None
feather : None
xlsxwriter : 3.1.9
lxml.etree : 4.9.3
html5lib : 1.1
pymysql : 1.4.6
psycopg2 : 2.9.7
jinja2 : 3.1.2
IPython : 8.17.2
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.12.2
bottleneck : 1.3.7
dataframe-api-compat : None
fastparquet : 2023.10.1
fsspec : 2023.10.0
gcsfs : 2023.10.0
matplotlib : 3.8.1
numba : 0.58.1
numexpr : 2.8.7
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.1
pyreadstat : 1.2.4
python-calamine : None
pyxlsb : 1.0.10
s3fs : 2023.10.0
scipy : 1.11.3
sqlalchemy : 2.0.23
tables : 3.9.1
tabulate : 0.9.0
xarray : 2023.11.0
xlrd : 2.0.1
zstandard : 0.22.0
tzdata : 2023.3
qtpy : None
pyqt5 : None

[jbrockmendel]

during conversion PeriodIndex.to_timestamp freq in DatetimeIndex unexpectedly depends on len of data. Shouldn't freqs in all examples above be equal 'QS-OCT' and 'MS', but not None?

freq unfortunately means something different for PeriodIndex than it does for DatetimeIndex, so we cannot infer the result freq directly from the PeriodIndex's dtype, xref #47227

[natmokval]

freq unfortunately means something different for PeriodIndex than it does for DatetimeIndex, so we cannot infer the result freq directly from the PeriodIndex's dtype, xref #47227

thanks for the comment. Seems like when we apply to_timestamp freq in DatetimeIndex changes if we change len of data in PeriodIndex, e.g.

data = ['2012-01', '2012-02', '2012-03']
per = pd.PeriodIndex(data=data, dtype='period[M]')
dti = per.to_timestamp(how='start')
print(dti.freq) # <MonthBegin>


data = ['2012-01', '2012-02']
per = pd.PeriodIndex(data, dtype='period[M]')
dti = per.to_timestamp(how='start')
print(dti.freq) # None

if len(data) < 3, then freq = None, otherwise freq != None
The same for dtype='period[Q]', dtype='period[Y]'
Is it the correct behaviour?

[jbrockmendel]

id guess this is tied to infer_freq only working with length>=3. im on record as thinknig #47227 is the best way to deal with this, but im open to other ideas