WIP: implement reductions for DatetimeArray/TimedeltaArray/PeriodArray
Some idiosyncrasies in signatures between Series vs Index make the parametrized test cases ugly.  Do we want to adapt the Index reductions to have a `skipna` kwarg like the Series and EA methods?

Still needs tests for timedelta and period dtypes.
Hello @jbrockmendel! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/arrays/datetimelike.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/core/arrays/datetimelike.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/period.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/core/indexes/period.py) !

 - There are no PEP8 issues in the file [`pandas/core/nanops.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/core/nanops.py) !

 - There are no PEP8 issues in the file [`pandas/core/series.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/core/series.py) !

 - There are no PEP8 issues in the file [`pandas/tests/indexes/datetimes/test_ops.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/tests/indexes/datetimes/test_ops.py) !

 - There are no PEP8 issues in the file [`pandas/tests/series/test_analytics.py`](https://github.com/jbrockmendel/pandas/blob/167989c9346dc6dfc3a387c8a4a6df76c75d4a01/pandas/tests/series/test_analytics.py) !

 Closing in favor of #24757.