REF: share start_time/end_time between Period/PeriodArray
- [ ] closes #xxxx
- [ ] tests added / passed
- [ ] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [ ] whatsnew entry

One thing that might make this undesirable is that the annotations on this are accurate for Period but not for PeriodArray.  Thoughts @simonjayhawkins 

lgtm. can you show the typing issue? > can you show the typing issue?

start_time and end_time are both annotated as returning Timestamp, but that is only accurate for Period, whereas for PeriodArray the annotation would be DatetimeArray.  mypy doesnt pick it up for reasons discussed on last week's call > > can you show the typing issue?
> 
> start_time and end_time are both annotated as returning Timestamp, but that is only accurate for Period, whereas for PeriodArray the annotation would be DatetimeArray. mypy doesnt pick it up for reasons discussed on last week's call

ok