This is a difficult question because we know so little about your particular system. They do vary quite a bit. There are some standard techniques used to troubleshoot problems, some that you may already know. One standard approach is to simplify the system by switching off or disconnecting some features one by one until the problem goes away. Doing this one by one may help isolate what is causing the problem. For example, most alarm panels have various sensors wired to them, often split up into zones. It is usually a good idea to first disconnect (or switch off via the keyboard) a few sensors at a time, like perhaps one zone, and see if the problem goes away. If it does, then perhaps we can say that the sensors in that zone or circuit are faulty or are being triggered somehow. Don't dismiss the possibility that everything is working correctly but a bug or rodent is actually running in front or inside of a motion sensor. My neighbor's garage alarm kept going off while he was away and I was watching the property. One day, when the alarm went off, I studied what was happening through a window instead of going inside the garage. I saw a rat running on a shelf right in front of one of the motion sensors!
One aspect is, does your problem occur only now and then? Can you make the problem happen immediately? If you can, you are in a good position to disable one zone at a time until the problem doesn't happen. If it doesn't happen so regularly, you may have to do this idea but be more patient about waiting too see if the problem is still there or not. You may have to disable one part of the system then wait a few days to see if that resolved it.
I'm not an alarm technician. You should consider asking your question on a forum that is specifically about alarm systems, where such technicians may be willing to lend a hand. Or you may find a forum of DIY enthusiasts who know these systems pretty well. I did a quick Google and found a few (I don't know if any of these are any good)
http://www.doityourself.com/forum/electronic-home-security-systems-alarms-devices-87/
http://forum.smarthome.com/forum.asp?FORUM_ID=11
http://www.shieldlab.com/forum/
and there appear to be others too. Often, when you come across a forum that is mostly frequented by actual security technicians, (the "pros"), the first thing they will advise is "hire a pro technician" to come and figure out the problem. While this approach is expensive in dollars, it is often the best use of your time and energy.