Yes, it is possible to close tickets automatically after a set period of time. Set this up according to these steps:
First navigate to Settings > Shared inbox and activate the slider ‘Close tickets automatically’ under 'Preferences'.
Choose after how many days you want the ticket to be closed automatically. If you choose 14 days here for example, tickets with the status ‘waiting for customer’ will be closed automatically if the last message is older than 14 days.
You can also define some templates for automatically closing tickets:
Navigate to Settings > Shared inbox > Templates for automatically closing tickets.
Here you can add automatic answers to send to your customers before closing the ticket.