No alarm as in you're not paying for the service?
...or no alarm, as in you don't have a single piece of an alarm system anywhere in the house?
I hear it all the time. "I don't have an alarm system." Yet when I go downstairs, I find one that the previous home owners installed and the new owners didn't know about.
Just because it isn't paid for monitoring, if it's connected in any way to the phone line, it can still be causing a problem.