id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1326238990,I_kwDOAMm_X85PDM0O,6870,`rolling_exp` loses coords,5635139,closed,0,,,4,2022-08-02T18:27:44Z,2023-09-19T01:13:23Z,2023-09-19T01:13:23Z,MEMBER,,,,"### What happened?

We lose the time coord here — `Dimensions without coordinates: time`:

```python
ds = xr.tutorial.load_dataset(""air_temperature"")
ds.rolling_exp(time=5).mean()

<xarray.Dataset>
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
  * lon      (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0
Dimensions without coordinates: time
Data variables:
    air      (time, lat, lon) float32 241.2 242.5 243.5 ... 296.4 296.1 295.7
```

(I realize I wrote this, I didn't think this used to happen, but either it always did or I didn't write good enough tests... mea culpa)

### What did you expect to happen?

We keep the time coords, like we do for normal `rolling`:

```python
In [2]: ds.rolling(time=5).mean()
Out[2]:
<xarray.Dataset>
Dimensions:  (lat: 25, lon: 53, time: 2920)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
  * lon      (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0
  * time     (time) datetime64[ns] 2013-01-01 ... 2014-12-31T18:00:00
```

### Minimal Complete Verifiable Example

```Python
(as above)
```


### MVCE confirmation

- [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [X] Complete example — the example is self-contained, including all data and the text of any traceback.
- [X] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [X] New issue — a search of GitHub Issues suggests this is not a duplicate.

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

<details>


INSTALLED VERSIONS
------------------
commit: None
python: 3.9.13 (main, May 24 2022, 21:13:51)
[Clang 13.1.6 (clang-1316.0.21.2)]
python-bits: 64
OS: Darwin
OS-release: 21.6.0
machine: arm64
processor: arm
byteorder: little
LC_ALL: en_US.UTF-8
LANG: None
LOCALE: ('en_US', 'UTF-8')
libhdf5: None
libnetcdf: None

xarray: 2022.6.0
pandas: 1.4.3
numpy: 1.21.6
scipy: 1.8.1
netCDF4: None
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: 2.12.0
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: 2021.12.0
distributed: 2021.12.0
matplotlib: 3.5.1
cartopy: None
seaborn: None
numbagg: 0.2.1
fsspec: 2021.11.1
cupy: None
pint: None
sparse: None
flox: None
numpy_groupies: None
setuptools: 62.3.2
pip: 22.1.2
conda: None
pytest: 7.1.2
IPython: 8.4.0
sphinx: 4.3.2


</details>
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