The alert log can give you that
SQL> select originating_timestamp, message_text
2 from V$DIAG_ALERT_EXT
3 where message_text like 'Starting ORACLE instance%'
4 or message_text like 'Shutting down instance%'
5 order by 1;
ORIGINATING_TIMESTAMP MESSAGE_TEXT
---------------------------------------- ---------------------------------------------------
23-AUG-18 10.25.40.283000000 AM +08:00 Starting ORACLE instance (normal) (OS id: 15552)
23-AUG-18 10.27.04.385000000 AM +08:00 Shutting down instance (abort) (OS id: 12692)
23-AUG-18 10.27.34.552000000 AM +08:00 Starting ORACLE instance (normal) (OS id: 17084)
23-AUG-18 10.28.10.369000000 AM +08:00 Shutting down instance (immediate) (OS id: 1244)
23-AUG-18 10.28.11.388000000 AM +08:00 Shutting down instance: further logons disabled
23-AUG-18 10.28.42.738000000 AM +08:00 Starting ORACLE instance (normal) (OS id: 9700)
23-AUG-18 10.33.23.868000000 AM +08:00 Shutting down instance (immediate) (OS id: 6628)
23-AUG-18 10.33.24.888000000 AM +08:00 Shutting down instance: further logons disabled
23-AUG-18 10.34.04.662000000 AM +08:00 Starting ORACLE instance (restrict) (OS id: 2124)
23-AUG-18 10.37.21.561000000 AM +08:00 Shutting down instance (immediate) (OS id: 15896)