I have a  shell script that I want to run automatically every day at 08 AM, and I am not authorised to use the crontab because I don't have root permission 
My home directory is /home/user1/.
Any suggestions?
Even if you dont have root permission you can set cron job. Chcek these 2 commands as user1, if you can modify it or its throwing any error.
crontab -l
If you can see then try this as well:
crontab -e
If you can open and edit, then you can run that script with cron.
by adding this line:
*  08  *  *  *    /path/to/your/script
schedule automate shell script running not as ROOT