BUG: DatetimeIndex.insert on empty can preserve freq

doc/source/whatsnew/v1.1.0.rst

@@ -479,6 +479,7 @@ Indexing
 - Bug in :meth:`DataFrame.copy` _item_cache not invalidated after copy causes post-copy value updates to not be reflected (:issue:`31784`)
 - Bug in `Series.__getitem__` with an integer key and a :class:`MultiIndex` with leading integer level failing to raise ``KeyError`` if the key is not present in the first level (:issue:`33355`)
 - Bug in :meth:`DataFrame.iloc` when slicing a single column-:class:`DataFrame`` with ``ExtensionDtype`` (e.g. ``df.iloc[:, :1]``) returning an invalid result (:issue:`32957`)
+- Bug in :meth:`DatetimeIndex.insert` and :meth:`TimedeltaIndex.insert` causing index ``freq`` to be lost when setting an element into an empty :class:`Series` (:issue:33573`)
 
 Missing
 ^^^^^^^

pandas/core/indexes/datetimelike.py

@@ -941,6 +941,10 @@ def insert(self, loc, item):
                     freq = self.freq
                 elif (loc == len(self)) and item - self.freq == self[-1]:
                     freq = self.freq
+            elif self.freq is not None:
+                # Adding a single item to an empty index may preserve freq
+                if self.freq.is_on_offset(item):
+                    freq = self.freq
             item = item.asm8
 
         try:

pandas/tests/indexes/datetimes/test_insert.py

@@ -24,6 +24,20 @@ def test_insert_invalid_na(self, tz):
         with pytest.raises(TypeError, match="incompatible label"):
             idx.insert(0, np.timedelta64("NaT"))
 
+    def test_insert_empty_preserves_freq(self, tz_naive_fixture):
+        # GH#33573
+        tz = tz_naive_fixture
+        dti = DatetimeIndex([], tz=tz, freq="D")
+        item = Timestamp("2017-04-05").tz_localize(tz)
+
+        result = dti.insert(0, item)
+        assert result.freq == dti.freq
+
+        # But not when we insert an item that doesnt conform to freq
+        dti = DatetimeIndex([], tz=tz, freq="W-THU")
+        result = dti.insert(0, item)
+        assert result.freq is None
+
     def test_insert(self):
         idx = DatetimeIndex(["2000-01-04", "2000-01-01", "2000-01-02"], name="idx")
 

pandas/tests/indexes/timedeltas/test_insert.py

@@ -93,9 +93,15 @@ def test_insert_dont_cast_strings(self):
 
     def test_insert_empty(self):
         # Corner case inserting with length zero doesnt raise IndexError
+        # GH#33573 for freq preservation
         idx = timedelta_range("1 Day", periods=3)
         td = idx[0]
 
-        idx[:0].insert(0, td)
-        idx[:0].insert(1, td)
-        idx[:0].insert(-1, td)
+        result = idx[:0].insert(0, td)
+        assert result.freq == "D"
+
+        result = idx[:0].insert(1, td)
+        assert result.freq == "D"
+
+        result = idx[:0].insert(-1, td)
+        assert result.freq == "D"

pandas/tests/series/indexing/test_indexing.py

@@ -284,17 +284,21 @@ def test_setitem(datetime_series, string_series):
     expected = string_series.append(app)
     tm.assert_series_equal(s, expected)
 
+
+def test_setitem_empty_series():
     # Test for issue #10193
     key = pd.Timestamp("2012-01-01")
     series = pd.Series(dtype=object)
     series[key] = 47
     expected = pd.Series(47, [key])
     tm.assert_series_equal(series, expected)
 
+    # GH#33573 our index should retain its freq
     series = pd.Series([], pd.DatetimeIndex([], freq="D"), dtype=object)
     series[key] = 47
     expected = pd.Series(47, pd.DatetimeIndex([key], freq="D"))
     tm.assert_series_equal(series, expected)
+    assert series.index.freq == expected.index.freq
 
 
 def test_setitem_dtypes():