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BUG: ewm.sum() gives incorrect values when used with halflife parameter #51695

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@SmartLizard

Description

@SmartLizard

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

  • I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

df = pd.DataFrame(
{"t": pd.to_datetime(["2023-02-28 12:00:00", "2023-02-28 12:00:05", "2023-02-28 12:00:15"]),
 "s": [1.0, 0.0, 0.0],
})

>>> print(df["s"].ewm(halflife="5 seconds", times=df["t"]).sum())
0    1.00
1    0.50
2    0.25

>>> print(df["s"].ewm(halflife="5 days", times=df["t"]).sum())
0    1.00
1    0.50
2    0.25

Issue Description

pd.ewm.sum() does not use halflife parameter.

As I understand it, there are two series held inside ewm: the data values and the weights. The .sum() function should contain the sum of the products of the data values with their weights.

Expected Behavior

For the first example I expected:

1.01.0 = 1
1.0
0.5 + 0.01.0 = 0.5 (1 half life)
1.0
0.125 + 0.0 * 0.5 + 0.0 *1.0 = 0.125 (3 half lifes) - here ewm returns 0.25 instead of 0.125

For the second example I expected:
1.0
0.9999
0.9999
since the half life is 5 days and only a few seconds have elapsed.

Installed Versions

INSTALLED VERSIONS ------------------ commit : 2e218d1 python : 3.11.0.final.0 python-bits : 64 OS : Darwin OS-release : 20.6.0 Version : Darwin Kernel Version 20.6.0: Fri Dec 16 00:35:00 PST 2022; root:xnu-7195.141.49~1/RELEASE_X86_64 machine : x86_64 processor : i386 byteorder : little LC_ALL : None LANG : en_GB.UTF-8 LOCALE : en_GB.UTF-8

pandas : 1.5.3
numpy : 1.24.2
pytz : 2022.7.1
dateutil : 2.8.2
setuptools : 65.6.3
pip : 23.0.1
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
brotli : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
snappy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None
tzdata : None

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