Make TimedeltaIndex +/- pd.NaT return TimedeltaIndex

doc/source/whatsnew/v0.23.0.txt

@@ -270,6 +270,7 @@ Other API Changes
 - Subtraction of :class:`Series` with timezone-aware ``dtype='datetime64[ns]'`` with mis-matched timezones will raise ``TypeError`` instead of ``ValueError`` (issue:`18817`)
 - :class:`IntervalIndex` and ``IntervalDtype`` no longer support categorical, object, and string subtypes (:issue:`19016`)
 - The default ``Timedelta`` constructor now accepts an ``ISO 8601 Duration`` string as an argument (:issue:`19040`)
+- Addition or subtraction of ``NaT`` from :class:`TimedeltaIndex` will return ``TimedeltaIndex`` instead of ``DatetimeIndex`` (:issue:`19124`)
 
 .. _whatsnew_0230.deprecations:
 

pandas/core/indexes/timedeltas.py

@@ -403,7 +403,8 @@ def _add_datelike(self, other):
         # adding a timedeltaindex to a datetimelike
         from pandas import Timestamp, DatetimeIndex
         if other is NaT:
-            result = self._nat_new(box=False)
+            # GH#19124 pd.NaT is treated like a timedelta
+            return self._nat_new()
         else:
             other = Timestamp(other)
             i8 = self.asi8
@@ -413,12 +414,13 @@ def _add_datelike(self, other):
         return DatetimeIndex(result, name=self.name, copy=False)
 
     def _sub_datelike(self, other):
-        from pandas import DatetimeIndex
+        # GH#19124 Timedelta - datetime is not in general well-defined.
+        # We make an exception for pd.NaT, which in this case quacks
+        # like a timedelta.
         if other is NaT:
-            result = self._nat_new(box=False)
+            return self._nat_new()
         else:
             raise TypeError("cannot subtract a datelike from a TimedeltaIndex")
-        return DatetimeIndex(result, name=self.name, copy=False)
 
     def _add_offset_array(self, other):
         # Array/Index of DateOffset objects

pandas/tests/scalar/test_nat.py

@@ -302,14 +302,30 @@ def test_nat_arithmetic_index():
         tm.assert_index_equal(left - right, exp)
         tm.assert_index_equal(right - left, exp)
 
-    # timedelta
+    # timedelta # GH#19124
     tdi = TimedeltaIndex(['1 day', '2 day'], name='x')
-    exp = DatetimeIndex([NaT, NaT], name='x')
-    for (left, right) in [(NaT, tdi)]:
-        tm.assert_index_equal(left + right, exp)
-        tm.assert_index_equal(right + left, exp)
-        tm.assert_index_equal(left - right, exp)
-        tm.assert_index_equal(right - left, exp)
+    tdi_nat = TimedeltaIndex([NaT, NaT], name='x')
+
+    tm.assert_index_equal(tdi + NaT, tdi_nat)
+    tm.assert_index_equal(NaT + tdi, tdi_nat)
+    tm.assert_index_equal(tdi - NaT, tdi_nat)
+    tm.assert_index_equal(NaT - tdi, tdi_nat)
+
+
+@pytest.mark.xfail(reason='NaT - Series returns NaT.  This behavior was '
+                          'introduced somewhere between 0.22.0 and '
+                          '23fb3392adedd3a')
+def test_nat_arithmetic_series():
+    # GH#19124
+    tdi = TimedeltaIndex(['1 day', '2 day'], name='x')
+    tdi_nat = TimedeltaIndex([NaT, NaT], name='x')
+    ser = Series(tdi)
+    ser_nat = Series(tdi_nat)
+
+    tm.assert_series_equal(ser + NaT, ser_nat)
+    tm.assert_series_equal(NaT + ser, ser_nat)
+    tm.assert_series_equal(ser - NaT, ser_nat)
+    tm.assert_series_equal(NaT - ser, ser_nat)
 
 
 def test_nat_pinned_docstrings():