For quite a while unknown to me my script was not automatically running via the cron job I setup. After entering my email address in cpanel’s standard cron interface, the email I received said:
Status: 404 Not Found
No input file specified.
A few minutes of searching the net uncovered my mistake. I had a url variable on the command, which cause it not to work. Instead of
php /home/mysite/public_html/filename.php method=automated .
Exclude the question mark in the url variable and that made it work.