Comments by Rony Sur (Top 1 by date)

Probably not.You can set a cron job in your server to remove the orders placed before 7 days. I think you are aware about cron job. If not, just ask your hosting provider to setup one for you. You just need to create a page with a sql query.
The query will be like:
query("DELETE FROM TABLE_NAME WHERE datediff(now(), order_date) > 7");

Hope this will solve your problem