BUG: Series.dt.to_period returns wrong dtype on all-NaTs

[adbull]

Code Sample, a copy-pastable example if possible

Input:

print(pd.to_datetime(['2001']).to_series().dt.to_period('D').dtype)
print(pd.to_datetime(['NaT']).to_series().dt.to_period('D').dtype)

Output:

object
datetime64[ns]

Problem description

Calling .dt.to_period on an all-NaT series will return datetimes, not periods. This can easily cause programs to crash on unexpected inputs.

Expected Output

object
object

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None
python: 3.6.5.final.0
python-bits: 64
OS: Linux
OS-release: 4.14.14-200.fc26.x86_64
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: C
LANG: C
LOCALE: None.None

pandas: 0.23.0
pytest: 3.5.1
pip: 10.0.1
setuptools: 39.1.0
Cython: 0.28.2
numpy: 1.13.3
scipy: 0.19.1
pyarrow: None
xarray: None
IPython: 4.2.1
sphinx: 1.7.4
patsy: 0.5.0
dateutil: 2.7.2
pytz: 2018.4
blosc: None
bottleneck: 1.2.1
tables: 3.4.3
numexpr: 2.6.2
feather: None
matplotlib: 2.2.2
openpyxl: None
xlrd: 1.1.0
xlwt: None
xlsxwriter: None
lxml: None
bs4: 4.6.0
html5lib: 1.0.1
sqlalchemy: 1.2.7
pymysql: None
psycopg2: None
jinja2: 2.10
s3fs: None
fastparquet: 0.1.5
pandas_gbq: None
pandas_datareader: None

[mroeschke]

This looks fixed on master (as Series now supports period types). Could use a test.

In [40]: print(pd.to_datetime(['2001']).to_series().dt.to_period('D').dtype)
    ...: print(pd.to_datetime(['NaT']).to_series().dt.to_period('D').dtype)
period[D]
period[D]

In [41]: pd.__version__
Out[41]: '0.24.0rc1+1.g33f91d8f9'