Should ewm_mean preserve null values?

[MarcoGorelli]

Checks

• I have checked that this issue has not already been reported.
• I have confirmed this bug exists on the latest version of Polars.

Reproducible example

In [30]: pl.Series([5.6, None, 3.7]).ewm_mean(alpha=.1, adjust=False, ignore_nulls=False)
Out[30]:
shape: (3,)
Series: '' [f64]
[
        5.6
        5.6
        5.391209
]

Log output

No response

Issue description

The second element is null, but the result forward fills the previous one. I think there's no need to, though?

Without nulls, the formula would be:

• y_0 = x_0
• y_1 = weighted_average([x_1, y_0], weights=[alpha, 1-alpha])
• y_2 = weighted_average([x_2, y_1], weights=[alpha, 1-alpha])

If x_1 is null, then the null values are skipped, and the result is scaled appropriately:

• y_0 = x_0
• y_1 = ???
• y_2:
  • weighted_average([x_2, y_0], weights=[alpha, (1-alpha)**2]) if ignore_nulls=False
  • weighted_average([x_2, y_0], weights=[alpha, 1-alpha]) if ignore_nulls=True

y_1 isn't used anywhere in any calculation. It doesn't need to be forward-filled from y_0, right?

Expected behavior

I think null values should be preserved. So, the output should be (imo):

shape: (3,)
Series: '' [f64]
[
        5.6
        null
        5.391209
]

I don't think this needs to be configurable either, it's easy to just add .forward_fill() to an expression chain if you want the nulls filled

As for how to go about changing it, I don't know - maybe it's fair game as a clearly documented and called-out breaking 1.0 change?

Installed versions

--------Version info---------
Polars:               0.20.16
Index type:           UInt32
Platform:             Linux-5.15.146.1-microsoft-standard-WSL2-x86_64-with-glibc2.35
Python:               3.11.8 (main, Feb 25 2024, 16:39:33) [GCC 11.4.0]

----Optional dependencies----
adbc_driver_manager:  <not installed>
cloudpickle:          <not installed>
connectorx:           <not installed>
deltalake:            <not installed>
fastexcel:            <not installed>
fsspec:               <not installed>
gevent:               <not installed>
hvplot:               0.9.2
matplotlib:           3.8.3
numpy:                1.26.4
openpyxl:             <not installed>
pandas:               2.2.1
pyarrow:              15.0.1
pydantic:             2.6.1
pyiceberg:            <not installed>
pyxlsb:               <not installed>
sqlalchemy:           <not installed>
xlsx2csv:             <not installed>
xlsxwriter:           <not installed>

[wbeardall]

I'm inclined to agree here, I'd err on the side of adding a statement to the expression chain over adding increased complexity to the interface.