[TST]: Wrong Corr with Timedelta index

doc/source/whatsnew/v1.2.0.rst

@@ -499,6 +499,7 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrame.groupby.rolling` returning wrong values with partial centered window (:issue:`36040`).
 - Bug in :meth:`DataFrameGroupBy.rolling` returned wrong values with timeaware window containing ``NaN``. Raises ``ValueError`` because windows are not monotonic now (:issue:`34617`)
 - Bug in :meth:`Rolling.__iter__` where a ``ValueError`` was not raised when ``min_periods`` was larger than ``window`` (:issue:`37156`)
+- Using :meth:`Rolling.var()` instead of :meth:`Rolling.std()` avoids numerical issues for :meth:`Rolling.corr()` when :meth:`Rolling.var()` is still within floating point precision while :meth:`Rolling.std()` is not (:issue:`31286`)
 
 Reshaping
 ^^^^^^^^^

pandas/core/window/rolling.py

@@ -1906,8 +1906,10 @@ def _get_corr(a, b):
             b = b.rolling(
                 window=window, min_periods=self.min_periods, center=self.center
             )
-
-            return a.cov(b, **kwargs) / (a.std(**kwargs) * b.std(**kwargs))
+            # GH 31286: Through using var instead of std we can avoid numerical
+            # issues when the result of var is withing floating proint precision
+            # while std is not.
+            return a.cov(b, **kwargs) / (a.var(**kwargs) * b.var(**kwargs)) ** 0.5
 
         return flex_binary_moment(
             self._selected_obj, other._selected_obj, _get_corr, pairwise=bool(pairwise)

pandas/tests/window/test_rolling.py

@@ -1073,3 +1073,17 @@ def get_window_bounds(self, num_values, min_periods, center, closed):
     result = getattr(df.rolling(indexer), method)()
     expected = DataFrame({"values": expected})
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    ("index", "window"),
+    [([0, 1, 2, 3, 4], 2), (pd.date_range("2001-01-01", freq="D", periods=5), "2D")],
+)
+def test_rolling_corr_timedelta_index(index, window):
+    # GH: 31286
+    x = Series([1, 2, 3, 4, 5], index=index)
+    y = x.copy()
+    x[0:2] = 0.0
+    result = x.rolling(window).corr(y)
+    expected = Series([np.nan, np.nan, 1, 1, 1], index=index)
+    tm.assert_almost_equal(result, expected)