Time recording is done, based on something you work on: a work item. So that's the story, change, incident, etc.
It doesn't really make sense to record time spend on an epic, because those don't really have a begin/end.
However, if the business case is that they want to know how much time is spend on any non-work item, you could just calculate the time spend on all work items related to the epic/feature/etc.
Time worked is also used on user level with time sheets and such. Make sure you aren't duplicating user recorded time, but really just calculate the different work items.
