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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 : b7a220731e901777f9d0a8da05c770764477c336 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

Comment From: 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

Comment From: 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?

Comment From: 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