BUG: ensure consistent behavior of Index.is_all_dates (pandas-dev#19204)

Author: adam

doc/source/whatsnew/v1.1.0.rst

@@ -341,6 +341,7 @@ Indexing
 - Fix to preserve the ability to index with the "nearest" method with xarray's CFTimeIndex, an :class:`Index` subclass (`pydata/xarray#3751 <https://github.com/pydata/xarray/issues/3751>`_, :issue:`32905`).
 - Bug in :class:`Index` constructor where an unhelpful error message was raised for ``numpy`` scalars (:issue:`33017`)
 - Bug in :meth:`DataFrame.lookup` incorrectly raising an ``AttributeError`` when ``frame.index`` or ``frame.columns`` is not unique; this will now raise a ``ValueError`` with a helpful error message (:issue:`33041`)
+- Bug in :meth:`Index.is_all_dates` incorrectly returning ``False`` when inferred type of index was other dates than datetime (:issue:`19204`)
 
 Missing
 ^^^^^^^

pandas/core/indexes/base.py

@@ -1975,7 +1975,14 @@ def is_all_dates(self) -> bool:
         """
         Whether or not the index values only consist of dates.
         """
-        return is_datetime_array(ensure_object(self.values))
+        return self.inferred_type in [
+            "datetime64",
+            "datetime",
+            "date",
+            "timedelta64",
+            "timedelta",
+            "period",
+        ]
 
     # --------------------------------------------------------------------
     # Pickle Methods

pandas/tests/indexes/test_base.py

@@ -1206,6 +1206,22 @@ def test_is_object(self, index, expected):
     def test_is_all_dates(self, index, expected):
         assert index.is_all_dates is expected
 
+    @pytest.mark.parametrize(
+        "index",
+        [
+            "datetime",
+            "datetime-tz",
+            "period",
+            "timedelta",
+            "empty"
+        ],
+        indirect=["index"],
+    )
+    def test_is_all_dates_consistency(self, index):
+        # GH 19204
+        non_date = pd.Index(['not a date'])
+        assert index.is_all_dates == index.append(non_date)[:-1].is_all_dates
+
     def test_summary(self, indices):
         self._check_method_works(Index._summary, indices)