ENH: Consider adding alternative calculation of centered moving averages for even window size

[TomasBeuzen]

• I have checked that this issue has not already been reported (originally reported in the now quite old incorrect calculation of centered moving averages for even length series #14425 but reviving here with a more thorough description of the problem)

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

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Code Sample

The current rolling(window, center=True).mean() behaviour in Pandas first calculates the rolling mean and then shifts the result back to "center" the labels. This does not give the expected result (at least to me):

import pandas as pd
window_size = 2
df = pd.DataFrame([2, 6, 4, 2, 0, 1, 5, 3],
                  index=["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug"])
df.rolling(window=window_size).mean()

	0
Jan	nan
Feb	4
Mar	5
Apr	3
May	1
Jun	0.5
Jul	3
Aug	4

Problem description

For rolling averages with an even sized window (e.g., 2, 4, 6, 8, etc.) it is common to apply a moving average with window size = 2 (2 x MA) to the result of the original moving average output to line up results with the original index.

Here's an example animation showing the expected behaviour:

Expected Output

The following code achieves the above (correct?) behaviour:

(df.rolling(window=window_size).mean()
   .rolling(window=2).mean()
   .shift(-window_size // 2)
)

	0
Jan	nan
Feb	4.5
Mar	4
Apr	2
May	0.75
Jun	1.75
Jul	3.5
Aug	nan

Additional context

I'm not sure if this needs to be changed in the codebase as the above workaround is not too bad. But I wanted to document the issue here for anyone who encounters it. I'd also be happy to work on a PR if this did want to be implemented.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : f2c8480
python : 3.9.2.final.0
python-bits : 64
OS : Darwin
OS-release : 18.7.0
Version : Darwin Kernel Version 18.7.0: Tue Aug 20 16:57:14 PDT 2019; root:xnu-4903.271.2~2/RELEASE_X86_64
machine : x86_64
processor : i386
byteorder : little
LC_ALL : None
LANG : en_CA.UTF-8
LOCALE : en_CA.UTF-8

pandas : 1.2.3
numpy : 1.20.1
pytz : 2021.1
dateutil : 2.8.1
pip : 21.0.1
setuptools : 49.6.0.post20210108
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fsspec : None
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : None

[mroeschke]

pandas rolling center, as you mentioned, is purely just relabeling of the index (and has been the convention for a while)

https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.rolling.html

center : bool, default False

    Set the labels at the center of the window.

Your proposed definition of center could be added as well (as a new keyword argument I guess) as an alternative way to calculate any rolling.<agg_func>; probably good if the other core devs weigh in too