diff --git a/.gitignore b/.gitignore
index 88ebdb2d7..f47c62c6e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -120,6 +120,9 @@ venv.bak/
 # PyCharm project settings
 .idea/
 
+# VSCode project settings
+.vscode/
+
 # mkdocs documentation
 /site
 
diff --git a/pandas-stubs/core/frame.pyi b/pandas-stubs/core/frame.pyi
index cf825a2f3..fcd6b996a 100644
--- a/pandas-stubs/core/frame.pyi
+++ b/pandas-stubs/core/frame.pyi
@@ -1776,7 +1776,7 @@ class DataFrame(NDFrame, OpsMixin):
     @overload
     def rolling(
         self,
-        window: int | BaseOffset | BaseIndexer,
+        window: int | str | BaseOffset | BaseIndexer,
         min_periods: int | None = ...,
         center: _bool = ...,
         *,
@@ -1790,7 +1790,7 @@ class DataFrame(NDFrame, OpsMixin):
     @overload
     def rolling(
         self,
-        window: int | BaseOffset | BaseIndexer,
+        window: int | str | BaseOffset | BaseIndexer,
         min_periods: int | None = ...,
         center: _bool = ...,
         *,
diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index 94161ed2d..0a12a9a1b 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -86,6 +86,7 @@ from pandas._typing import (
     HashableT3,
     IgnoreRaise,
     IndexingInt,
+    IntervalClosedType,
     JoinHow,
     JsonSeriesOrient,
     Level,
@@ -1574,28 +1575,28 @@ class Series(IndexOpsMixin, NDFrame, Generic[S1]):
     @overload
     def rolling(
         self,
-        window: int | BaseOffset | BaseIndexer,
+        window: int | _str | BaseOffset | BaseIndexer,
         min_periods: int | None = ...,
         center: _bool = ...,
         *,
         win_type: _str,
         on: _str | None = ...,
         axis: SeriesAxisType = ...,
-        closed: _str | None = ...,
+        closed: IntervalClosedType | None = ...,
         step: int | None = ...,
         method: CalculationMethod = ...,
     ) -> Window[Series]: ...
     @overload
     def rolling(
         self,
-        window: int | BaseOffset | BaseIndexer,
+        window: int | _str | BaseOffset | BaseIndexer,
         min_periods: int | None = ...,
         center: _bool = ...,
         *,
         win_type: None = ...,
         on: _str | None = ...,
         axis: SeriesAxisType = ...,
-        closed: _str | None = ...,
+        closed: IntervalClosedType | None = ...,
         step: int | None = ...,
         method: CalculationMethod = ...,
     ) -> Rolling[Series]: ...
diff --git a/tests/test_windowing.py b/tests/test_windowing.py
index 8f3da3e34..bf0d88dbf 100644
--- a/tests/test_windowing.py
+++ b/tests/test_windowing.py
@@ -13,9 +13,13 @@
 
 from tests import check
 
+from pandas.tseries.frequencies import to_offset
+
 IDX = date_range("1/1/2000", periods=700, freq="D")
 S = Series(np.random.standard_normal(700))
 DF = DataFrame({"col1": S, "col2": S})
+S_DTI = Series(data=np.random.standard_normal(700), index=IDX)
+DF_DTI = DataFrame(data=np.random.standard_normal(700), index=IDX)
 
 
 def test_rolling_basic() -> None:
@@ -43,6 +47,22 @@ def test_rolling_basic_math() -> None:
     check(assert_type(DF.rolling(10).rank("max"), DataFrame), DataFrame)
 
 
+def test_rolling_datetime_index() -> None:
+    offset_1d = to_offset("1D")
+    assert offset_1d is not None
+
+    check(assert_type(DF_DTI.rolling("1D"), "Rolling[DataFrame]"), Rolling, DataFrame)
+    check(
+        assert_type(DF_DTI.rolling(offset_1d), "Rolling[DataFrame]"), Rolling, DataFrame
+    )
+    check(assert_type(S_DTI.rolling("1D"), "Rolling[Series]"), Rolling, Series)
+    check(
+        assert_type(S_DTI.rolling(offset_1d), "Rolling[Series]"),
+        Rolling,
+        Series,
+    )
+
+
 def test_rolling_apply() -> None:
     check(assert_type(DF.rolling(10).apply(np.mean), DataFrame), DataFrame)