ENH: support NaT values into datetime series for interpolation (#11701)

doc/source/whatsnew/v0.24.0.txt

@@ -182,6 +182,8 @@ Other Enhancements
 - :func:`to_timedelta` now supports iso-formated timedelta strings (:issue:`21877`)
 - :class:`Series` and :class:`DataFrame` now support :class:`Iterable` in constructor (:issue:`2193`)
 - :class:`DatetimeIndex` gained :attr:`DatetimeIndex.timetz` attribute. Returns local time with timezone information. (:issue:`21358`)
+- Implement interpolating ``NaT`` values in ``datetime`` series (:issue:`11701`)
+-
 
 .. _whatsnew_0240.api_breaking:
 

pandas/core/generic.py

@@ -6316,6 +6316,14 @@ def interpolate(self, method='linear', axis=0, limit=None, inplace=False,
             raise NotImplementedError("Interpolation with NaNs in the index "
                                       "has not been implemented. Try filling "
                                       "those NaNs before interpolating.")
+        is_datetime = False
+        datetime_timezone = None
+        if is_datetime64_any_dtype(_maybe_transposed_self):
+            _datetime_nat_values = _maybe_transposed_self.isnull()
+            datetime_timezone = _maybe_transposed_self.dt.tz
+            _maybe_transposed_self = _maybe_transposed_self.astype('int')
+            _maybe_transposed_self[_datetime_nat_values] = np.nan
+            is_datetime = True
         data = _maybe_transposed_self._data
         new_data = data.interpolate(method=method, axis=ax, index=index,
                                     values=_maybe_transposed_self, limit=limit,
@@ -6324,6 +6332,11 @@ def interpolate(self, method='linear', axis=0, limit=None, inplace=False,
                                     inplace=inplace, downcast=downcast,
                                     **kwargs)
 
+        if is_datetime:
+            new_data = self._constructor(new_data)
+            new_data = pd.to_datetime(new_data, utc=True).dt.tz_convert(
+                datetime_timezone)
+
         if inplace:
             if axis == 1:
                 new_data = self._constructor(new_data).T._data

pandas/tests/series/test_missing.py

@@ -1317,3 +1317,16 @@ def test_series_interpolate_intraday(self):
         result = ts.reindex(new_index).interpolate(method='time')
 
         tm.assert_numpy_array_equal(result.values, exp.values)
+
+    @pytest.mark.parametrize("inplace", [True, False])
+    def test_series_interpolate_nat(self, tz_naive_fixture, inplace):
+        # GH 11701
+        expected = pd.Series(pd.date_range('2015-01-01',
+                                           '2015-01-30', tz=tz_naive_fixture))
+        result = expected.copy()
+        result[[3, 4, 5, 13, 14, 15]] = pd.NaT
+        if inplace:
+            result.interpolate(inplace=inplace)
+        else:
+            result = result.interpolate()
+        tm.assert_series_equal(result, expected)