BUG: DatetimeIndex.intersection losing freq and tz

doc/source/whatsnew/v1.1.0.rst

@@ -458,6 +458,7 @@ Datetimelike
 - Bug in :class:`Timestamp` arithmetic when adding or subtracting a ``np.ndarray`` with ``timedelta64`` dtype (:issue:`33296`)
 - Bug in :meth:`DatetimeIndex.to_period` not infering the frequency when called with no arguments (:issue:`33358`)
 - Bug in :meth:`DatetimeIndex.tz_localize` incorrectly retaining ``freq`` in some cases where the original freq is no longer valid (:issue:`30511`)
+- Bug in :meth:`DatetimeIndex.intersection` losing ``freq`` and timezone in some cases (:issue:`33604`)
 
 Timedelta
 ^^^^^^^^^

pandas/core/indexes/datetimelike.py

@@ -724,10 +724,10 @@ def intersection(self, other, sort=False):
         start = right[0]
 
         if end < start:
-            return type(self)(data=[])
+            return type(self)(data=[], dtype=self.dtype, freq=self.freq)
         else:
             lslice = slice(*left.slice_locs(start, end))
-            left_chunk = left.values[lslice]
+            left_chunk = left._values[lslice]
             return self._shallow_copy(left_chunk)
 
     def _can_fast_union(self, other) -> bool:

pandas/tests/indexes/datetimes/test_indexing.py

@@ -75,8 +75,9 @@ def test_getitem(self):
     def test_dti_business_getitem(self):
         rng = pd.bdate_range(START, END)
         smaller = rng[:5]
-        exp = DatetimeIndex(rng.view(np.ndarray)[:5])
+        exp = DatetimeIndex(rng.view(np.ndarray)[:5], freq="B")
         tm.assert_index_equal(smaller, exp)
+        assert smaller.freq == exp.freq
 
         assert smaller.freq == rng.freq
 
@@ -102,8 +103,9 @@ def test_dti_business_getitem_matplotlib_hackaround(self):
     def test_dti_custom_getitem(self):
         rng = pd.bdate_range(START, END, freq="C")
         smaller = rng[:5]
-        exp = DatetimeIndex(rng.view(np.ndarray)[:5])
+        exp = DatetimeIndex(rng.view(np.ndarray)[:5], freq="C")
         tm.assert_index_equal(smaller, exp)
+        assert smaller.freq == exp.freq
         assert smaller.freq == rng.freq
 
         sliced = rng[::5]

pandas/tests/indexes/datetimes/test_setops.py

@@ -269,14 +269,34 @@ def test_intersection(self, tz, sort):
             assert result.freq is None
             assert result.tz == expected.tz
 
-    def test_intersection_empty(self):
+    # parametrize over both anchored and non-anchored freqs, as they
+    #  have different code paths
+    @pytest.mark.parametrize("freq", ["T", "B"])
+    def test_intersection_empty(self, tz_aware_fixture, freq):
         # empty same freq GH2129
-        rng = date_range("6/1/2000", "6/15/2000", freq="T")
+        tz = tz_aware_fixture
+        rng = date_range("6/1/2000", "6/15/2000", freq=freq, tz=tz)
         result = rng[0:0].intersection(rng)
         assert len(result) == 0
+        assert result.freq == rng.freq
 
         result = rng.intersection(rng[0:0])
         assert len(result) == 0
+        assert result.freq == rng.freq
+
+        # no overlap GH#33604
+        result = rng[:3].intersection(rng[-3:])
+        tm.assert_index_equal(result, rng[:0])
+        if freq != "T":
+            # We don't preserve freq on non-anchored offsets
+            assert result.freq == rng.freq
+
+        # swapped left and right
+        result = rng[-3:].intersection(rng[:3])
+        tm.assert_index_equal(result, rng[:0])
+        if freq != "T":
+            # We don't preserve freq on non-anchored offsets
+            assert result.freq == rng.freq
 
     def test_intersection_bug_1708(self):
         from pandas import DateOffset
@@ -450,6 +470,7 @@ def test_intersection_bug(self):
         b = bdate_range("12/10/2011", "12/20/2011")
         result = a.intersection(b)
         tm.assert_index_equal(result, b)
+        assert result.freq == b.freq
 
     def test_month_range_union_tz_pytz(self, sort):
         from pytz import timezone
@@ -527,3 +548,4 @@ def test_intersection_bug(self):
         b = bdate_range("12/10/2011", "12/20/2011", freq="C")
         result = a.intersection(b)
         tm.assert_index_equal(result, b)
+        assert result.freq == b.freq

pandas/tests/indexes/timedeltas/test_setops.py

@@ -106,6 +106,7 @@ def test_intersection_bug_1708(self):
         result = index_1 & index_2
         expected = timedelta_range("1 day 01:00:00", periods=3, freq="h")
         tm.assert_index_equal(result, expected)
+        assert result.freq == expected.freq
 
     def test_intersection_equal(self, sort):
         # GH 24471 Test intersection outcome given the sort keyword
@@ -182,7 +183,7 @@ def test_intersection(self, rng, expected, sort):
                 TimedeltaIndex(["2 hour", "5 hour", "5 hour", "1 hour"], name="other"),
                 TimedeltaIndex(["1 hour", "2 hour"], name=None),
             ),
-            # reveresed index
+            # reversed index
             (
                 TimedeltaIndex(["1 hour", "2 hour", "4 hour", "3 hour"], name="idx")[
                     ::-1
@@ -200,7 +201,7 @@ def test_intersection_non_monotonic(self, rng, expected, sort):
         tm.assert_index_equal(result, expected)
         assert result.name == expected.name
 
-        # if reveresed order, frequency is still the same
+        # if reversed order, frequency is still the same
         if all(base == rng[::-1]) and sort is None:
             assert isinstance(result.freq, Hour)
         else: