BUG: .quantile with empty temporal data

Author: mroeschke

pandas/core/arrays/_mixins.py

@@ -512,9 +512,7 @@ def _quantile(
         else:
             # e.g. test_quantile_empty we are empty integer dtype and res_values
             #  has floating dtype
-            # TODO: technically __init__ isn't defined here.
-            #  Should we raise NotImplementedError and handle this on NumpyEA?
-            return type(self)(res_values)  # type: ignore[call-arg]
+            return type(self)._from_sequence(res_values)  # type: ignore[call-arg]
 
     # ------------------------------------------------------------------------
     # numpy-like methods

pandas/tests/series/methods/test_quantile.py

@@ -245,3 +245,10 @@ def test_quantile_dtype_size(self, any_int_ea_dtype):
         result = ser.quantile([0.1, 0.5])
         expected = Series([1, 1], dtype=any_int_ea_dtype, index=[0.1, 0.5])
         tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("typ", ["datetime64", "timedelta64"])
+def test_quantile_empty_datetimelike(typ, unit):
+    ser = Series([], dtype=f"{typ}[{unit}]")
+    result = ser.quantile()
+    assert result is pd.NaT