No.3456
I assume this is VPS or similar
in this case whomever owns your server ultimately can of course, modify something such that your automated system cannot tell, or in such a way that the local checking system doesnt trigger an alarm to you, if they are careful.
a reliable way would be to create say, a weekly file listing hashes of 'major files' on the system. kernel, libraries, data, config files, what have you. This could be a cron job.
On a seperate system you trust, you either sync this file each time, and check for hash changes, or even you could hash that file and keep a 'system hash'.
I just dont like the idea of maintaining the ultimate monitoring be on the untrusted system.