ERR: Raise TypeError for groupby.var with timeldeta

doc/source/whatsnew/v2.1.0.rst

@@ -401,7 +401,7 @@ Groupby/resample/rolling
   the function operated on the whole index rather than each element of the index. (:issue:`51979`)
 - Bug in :meth:`DataFrameGroupBy.apply` causing an error to be raised when the input :class:`DataFrame` was subset as a :class:`DataFrame` after groupby (``[['a']]`` and not ``['a']``) and the given callable returned :class:`Series` that were not all indexed the same. (:issue:`52444`)
 - Bug in :meth:`GroupBy.groups` with a datetime key in conjunction with another key produced incorrect number of group keys (:issue:`51158`)
-- Bug in :meth:`GroupBy.var` failing to raise ``TypeError`` when called with datetime64 or :class:`PeriodDtype` values (:issue:`52128`)
+- Bug in :meth:`GroupBy.var` failing to raise ``TypeError`` when called with datetime64, timedelta64 or :class:`PeriodDtype` values (:issue:`52128`, :issue:`53045`)
 -
 
 Reshaping

pandas/core/arrays/datetimelike.py

@@ -1583,7 +1583,7 @@ def _groupby_op(
                 )
         else:
             # timedeltas we can add but not multiply
-            if how in ["prod", "cumprod", "skew"]:
+            if how in ["prod", "cumprod", "skew", "var"]:
                 raise TypeError(f"timedelta64 type does not support {how} operations")
 
         # All of the functions implemented here are ordinal, so we can

pandas/tests/groupby/test_raises.py

@@ -66,6 +66,19 @@ def df_with_datetime_col():
     return df
 
 
+@pytest.fixture
+def df_with_timedelta_col():
+    df = DataFrame(
+        {
+            "a": [1, 1, 1, 1, 1, 2, 2, 2, 2],
+            "b": [3, 3, 4, 4, 4, 4, 4, 3, 3],
+            "c": range(9),
+            "d": datetime.timedelta(days=1),
+        }
+    )
+    return df
+
+
 @pytest.fixture
 def df_with_cat_col():
     df = DataFrame(
@@ -323,6 +336,21 @@ def test_groupby_raises_datetime_np(
     _call_and_check(klass, msg, how, gb, groupby_func_np, tuple())
 
 
+@pytest.mark.parametrize("func", ["prod", "cumprod", "skew", "var"])
+def test_groupby_raises_timedelta(func, df_with_timedelta_col):
+    df = df_with_timedelta_col
+    gb = df.groupby(by="a")
+
+    _call_and_check(
+        TypeError,
+        "timedelta64 type does not support .* operations",
+        "method",
+        gb,
+        func,
+        [],
+    )
+
+
 @pytest.mark.parametrize("how", ["method", "agg", "transform"])
 def test_groupby_raises_category(
     how, by, groupby_series, groupby_func, using_copy_on_write, df_with_cat_col