BUG: rolling.corr() produces wrong result with equal values

[byospe]

Code Sample, a copy-pastable example if possible

s = pd.Series([1,1,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,7,0,0,0])
pd.rolling_corr(s,s,6)

Problem description

rolling_corr is producing the wrong result:

python
pd.rolling_corr(s,s,6)

0 NaN
1 NaN
2 NaN
3 NaN
4 NaN
5 1.0
6 1.0
7 1.0
8 1.0
9 0.0
10 0.0
11 0.0
12 0.0
13 0.0
14 0.0
15 0.0
16 0.0
17 0.0
18 0.0
19 0.0
20 0.0
21 0.0
22 0.0
23 0.0
24 0.0
25 0.0
26 1.0
27 1.0
28 1.0
29 1.0
30 1.0
31 1.0
32 1.0
33 1.0

This should have nan's instead of 0's for windows with static data.

Expected Output

Output of pd.show_versions()

[paste the output of pd.show_versions() here below this line]

INSTALLED VERSIONS

commit: None
python: 3.5.3.final.0
python-bits: 64
OS: Linux
OS-release: 4.1.35-pv-ts2
machine: x86_64
processor:
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.20.3
pytest: 3.0.7
pip: 9.0.1
setuptools: 36.4.0
Cython: 0.25.2
numpy: 1.11.3
scipy: 0.19.0
xarray: None
IPython: 5.3.0
sphinx: 1.6.2
patsy: 0.4.1
dateutil: 2.6.0
pytz: 2017.2
blosc: None
bottleneck: None
tables: 3.3.0
numexpr: 2.6.2
feather: None
matplotlib: 1.5.1
openpyxl: 2.4.8
xlrd: 1.0.0
xlwt: None
xlsxwriter: 0.9.8
lxml: None
bs4: 4.5.3
html5lib: 0.999
sqlalchemy: 1.1.10
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
pandas_gbq: None
pandas_datareader: None

[jreback]

I think this is a very similar problem to #18044, recently fixed in #18085. We are NaNing out values that are numerically very close to zero (e.g. denominator is std * std), but in this case we are missing it because they are not identically zero.

[jreback]

@byospe want to try a PR to fix?

[Licht-T]

I am working on this and the fixing is almost done.
Seems that the numerical calculation matter.
https://github.com/pandas-dev/pandas/blob/master/pandas/core/window.py#L1064