Bug cov nat

pandas/core/frame.py

@@ -11239,6 +11239,12 @@ def cov(
         c -0.150812  0.191417  0.895202
         """
         data = self._get_numeric_data() if numeric_only else self
+        if data.select_dtypes(include=[np.datetime64, np.timedelta64]).shape[1] > 0:
+            msg = (
+                "DataFrame contains columns with dtype datetime64[ns] "
+                "or timedelta64[ns], which are not supported for cov."
+            )
+            raise TypeError(msg)
         cols = data.columns
         idx = cols.copy()
         mat = data.to_numpy(dtype=float, na_value=np.nan, copy=False)

pandas/tests/frame/test_reductions.py

@@ -1907,6 +1907,39 @@ def test_df_empty_nullable_min_count_1(self, opname, dtype, exp_dtype):
         expected = Series([pd.NA, pd.NA], dtype=exp_dtype, index=Index([0, 1]))
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "data",
+        [
+            {"a": [0, 1, 2], "b": [pd.NaT, pd.NaT, pd.NaT]},
+            {"a": [0, 1, 2], "b": [Timestamp("1990-01-01"), pd.NaT, pd.NaT]},
+            {
+                "a": [0, 1, 2],
+                "b": [
+                    Timestamp("1990-01-01"),
+                    Timestamp("1991-01-01"),
+                    Timestamp("1992-01-01"),
+                ],
+            },
+            {
+                "a": [0, 1, 2],
+                "b": [pd.Timedelta("1 days"), pd.Timedelta("2 days"), pd.NaT],
+            },
+            {
+                "a": [0, 1, 2],
+                "b": [
+                    pd.Timedelta("1 days"),
+                    pd.Timedelta("2 days"),
+                    pd.Timedelta("3 days"),
+                ],
+            },
+        ],
+    )
+    def test_df_cov_pd_nat(self, data):
+        # GH #53115
+        df = DataFrame(data)
+        with pytest.raises(TypeError, match="not supported for cov"):
+            df.cov()
+
 
 def test_sum_timedelta64_skipna_false():
     # GH#17235