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?
In a pinch, you can use at(1). Make sure the program you run reschedules the at job.  Warning: this goes to heck if the machine is down for any length of time.
schedule automate shell script running not as ROOT