Partial Dates within Craft
I'd set this up with regular date fields. You can then display the dates in whatever format you require on the front end using Twig's date formatting filter.

With the data stored as dates you can do a lot more with it compared to simply storing strings.

If you need to show a date range, such as "2013-2015" then it would probably be best to use 2 fields. A "date from" and a "date to" field. You could then use some logic to display one, or both, depending on whether there was something in the "date to" field.