I hope you don't mind me stepping in to add some information for other community members looking at this question.
Jira Cloud does not offer a native "archiving" functionality, same applies to Jira Server. (subject to change)
It is worth mentioning Jira Data Center offers this feature.
Hello there Cloud Community members! Today, we’re thrilled to announce Jira Service Management, the next generation of Jira Service Desk. Jira Service Management touts advancements in IT service ...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events