BUG: Fix groupby nunique with NaT (pandas-dev#17624)

Author: Licht-T

doc/source/whatsnew/v0.21.0.txt

@@ -552,6 +552,7 @@ Groupby/Resample/Rolling
 - Bug in ``Series.resample(...).apply()`` where an empty ``Series`` modified the source index and did not return the name of a ``Series`` (:issue:`14313`)
 - Bug in ``.rolling(...).apply(...)`` with a ``DataFrame`` with a ``DatetimeIndex``, a ``window`` of a timedelta-convertible and ``min_periods >= 1` (:issue:`15305`)
 - Bug in ``DataFrame.groupby`` where index and column keys were not recognized correctly when the number of keys equaled the number of elements on the groupby axis (:issue:`16859`)
+- Bug in ``groupby.nunique()`` with ``TimeGrouper`` which cannot handle ``NaT`` correctly (:issue:`17575`)
 
 Sparse
 ^^^^^^

pandas/core/groupby.py

@@ -3177,7 +3177,13 @@ def nunique(self, dropna=True):
 
         out = np.add.reduceat(inc, idx).astype('int64', copy=False)
         if len(ids):
-            res = out if ids[0] != -1 else out[1:]
+            # NaN/NaT group exists if the head of ids is -1,
+            # so remove it from res and exclude its index from idx
+            if ids[0] == -1:
+                res = out[1:]
+                idx = idx[np.flatnonzero(idx)]
+            else:
+                res = out
         else:
             res = out[1:]
         ri = self.grouper.result_index

pandas/tests/groupby/test_timegrouper.py

@@ -608,3 +608,16 @@ def test_first_last_max_min_on_time_data(self):
         assert_frame_equal(grouped_ref.min(), grouped_test.min())
         assert_frame_equal(grouped_ref.first(), grouped_test.first())
         assert_frame_equal(grouped_ref.last(), grouped_test.last())
+
+    def test_nunique_with_timegrouper_and_nat(self):
+        # GH 17575
+        test = pd.DataFrame({
+            'time': [Timestamp('2016-06-28 09:35:35'),
+                     pd.NaT,
+                     Timestamp('2016-06-28 16:46:28')],
+            'data': ['1', '2', '3']})
+
+        grouper = pd.TimeGrouper(key='time', freq='h')
+        result = test.groupby(grouper)['data'].nunique()
+        expected = test[test.time.notnull()].groupby(grouper)['data'].nunique()
+        tm.assert_series_equal(result, expected)