.min() on a series of NaTs returns nan, while .max() returns NaT

[ericstarr]

Code Sample

s = pd.Series([pd.NaT, pd.NaT])

# Returns nan
s.min()

# Returns NaT
s.max()

Problem description

Calling .min() on an series of NaT returns nan. I would expect this to return NaT to as to keep the type the same. Also, whether it returns nan or NaT, I would expect it to be consistent with .max(). I'm on version 0.22, not 0.23, so maybe it was fixed in the latest version, but I didn't see an issue addressing it.

Expected Output

I would expect that the s.min() call would also return NaT.

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None
python: 3.5.4.final.0
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 45 Stepping 7, GenuineIntel
byteorder: little
LC_ALL: None
LANG: None
LOCALE: None.None

pandas: 0.22.0
pytest: None
pip: 10.0.1
setuptools: 40.2.0
Cython: None
numpy: 1.15.1
scipy: 1.1.0
pyarrow: None
xarray: None
IPython: 6.5.0
sphinx: None
patsy: None
dateutil: 2.7.3
pytz: 2018.5
blosc: None
bottleneck: None
tables: None
numexpr: None
feather: None
matplotlib: None
openpyxl: None
xlrd: None
xlwt: None
xlsxwriter: None
lxml: None
bs4: None
html5lib: 1.0.1
sqlalchemy: 1.2.11
pymysql: None
psycopg2: None
jinja2: 2.10
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None

[mroeschke]

Thanks for the report. I am seeing this behavior on master too. Also looks similar to #10390.

Investigations and PRs welcome!