SharePoint 2013 offers the option of audit logs:
One of the settings available is to trim the audit logs and optionally save the trimmed data into a library. As the above article states the default is every 30 days, but you can change the log retention to some other value.
If you do want to change your log retention to something other than the default (say 7 days) then you might find that your logs don’t appear to be getting trimmed. Make sure that you also set the schedule of the corresponding timer job to match your retention schedule.
Each web application will have its own Audit Log Trimming job. The default schedule for the timer job is monthly, so if you want to have a retention of 7 days then set the schedule of the timer jobs to weekly and test the results.