BUG: Rolling.__iter__ includes on index columns in the result (#41405)

Co-authored-by: Jeff Reback <[email protected]>

Author: mroeschke

doc/source/whatsnew/v1.3.0.rst

@@ -1037,6 +1037,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupBy.__getitem__` with non-unique columns incorrectly returning a malformed :class:`SeriesGroupBy` instead of :class:`DataFrameGroupBy` (:issue:`41427`)
 - Bug in :meth:`DataFrameGroupBy.transform` with non-unique columns incorrectly raising ``AttributeError`` (:issue:`41427`)
 - Bug in :meth:`Resampler.apply` with non-unique columns incorrectly dropping duplicated columns (:issue:`41445`)
+- Bug in :meth:`DataFrame.rolling.__iter__` where ``on`` was not assigned to the index of the resulting objects (:issue:`40373`)
 - Bug in :meth:`DataFrameGroupBy.transform` and :meth:`DataFrameGroupBy.agg` with ``engine="numba"`` where ``*args`` were being cached with the user passed function (:issue:`41647`)
 
 Reshaping

pandas/core/window/rolling.py

@@ -291,6 +291,7 @@ def __repr__(self) -> str:
 
     def __iter__(self):
         obj = self._create_data(self._selected_obj)
+        obj = obj.set_axis(self._on)
         indexer = self._get_window_indexer()
 
         start, end = indexer.get_window_bounds(

pandas/tests/window/test_rolling.py

@@ -742,7 +742,7 @@ def test_iter_rolling_dataframe(df, expected, window, min_periods):
     ],
 )
 def test_iter_rolling_on_dataframe(expected, window):
-    # GH 11704
+    # GH 11704, 40373
     df = DataFrame(
         {
             "A": [1, 2, 3, 4, 5],
@@ -751,7 +751,9 @@ def test_iter_rolling_on_dataframe(expected, window):
         }
     )
 
-    expected = [DataFrame(values, index=index) for (values, index) in expected]
+    expected = [
+        DataFrame(values, index=df.loc[index, "C"]) for (values, index) in expected
+    ]
     for (expected, actual) in zip(expected, df.rolling(window, on="C")):
         tm.assert_frame_equal(actual, expected)