BUG: rolling.corr with MultiIndex columns

doc/source/whatsnew/v1.4.0.rst

@@ -408,6 +408,7 @@ Groupby/resample/rolling
 - Bug in :meth:`pandas.DataFrame.rolling` operation along rows (``axis=1``) incorrectly omits columns containing ``float16`` and ``float32`` (:issue:`41779`)
 - Bug in :meth:`Resampler.aggregate` did not allow the use of Named Aggregation (:issue:`32803`)
 - Bug in :meth:`Series.rolling` when the :class:`Series` ``dtype`` was ``Int64`` (:issue:`43016`)
+- Bug in :meth:`DataFrame.rolling.corr` when the :class:`DataFrame` columns was a :class:`MultiIndex` (:issue:`21157`)
 
 Reshaping
 ^^^^^^^^^

pandas/core/window/common.py

@@ -83,8 +83,22 @@ def dataframe_from_int_dict(data, frame_template):
                         # mypy needs to know columns is a MultiIndex, Index doesn't
                         # have levels attribute
                         arg2.columns = cast(MultiIndex, arg2.columns)
-                        result.index = MultiIndex.from_product(
-                            arg2.columns.levels + [result_index]
+                        # GH 21157: Equivalent to MultiIndex.from_product(
+                        # <unique combinations of arg2.columns.levels>, [result_index]
+                        # )
+                        # A normal MultiIndex.from_product will produce too many
+                        # combinations.
+                        idx_codes, idx_uniques = result_index.factorize()
+                        result_levels = list(arg2.columns.levels) + [idx_uniques]
+                        result_codes = [
+                            np.tile(code, int(len(result) / len(code)))
+                            for code in arg2.columns.codes
+                        ] + [np.tile(idx_codes, int(len(result) / len(idx_codes)))]
+                        result_names = list(arg2.columns.names) + [result_index.name]
+                        result.index = MultiIndex(
+                            levels=result_levels,
+                            codes=result_codes,
+                            names=result_names,
                         )
                         # GH 34440
                         num_levels = len(result.index.levels)

pandas/tests/window/test_rolling.py

@@ -1500,3 +1500,19 @@ def test_rolling_numeric_dtypes():
         dtype="float64",
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_multindex_columns_pairwise_func():
+    # GH 21157
+    columns = MultiIndex.from_arrays([["M", "N"], ["P", "Q"]], names=["a", "b"])
+    df = DataFrame(np.ones((5, 2)), columns=columns)
+    result = df.rolling(3).corr()
+    expected = DataFrame(
+        np.nan,
+        index=MultiIndex.from_arrays(
+            [np.repeat(np.arange(5), 2), ["M", "N"] * 5, ["P", "Q"] * 5],
+            names=[None, "a", "b"],
+        ),
+        columns=columns,
+    )
+    tm.assert_frame_equal(result, expected)