I have installed various makes models of Aftermarket car alarms (all of them are pretty much the same). Anyway the alarm will activate if:
1) You have pressed the on button on the remote.
2) You have a passive arming mode as mentioned by huskyfan (these can be disabled by moving a dip switch inside the alarm).
That being said most problems related to alarms would fall into the loose wiring category. The obvious culprits would be power & ground, but there are also wires to sense current drain, shock sensors, sound sensors ect.
If a power or ground wire breaks contact then the alarm brain will shut down..If the wires regains good contact then the alarm will automatically arm itself as a "default" mode .(ie it couldn't remember if it was on or off so it chooses to go on)
I can go into greater detail on each circuit, but I should first ask the following info:
1) Does the alarm work normally, or does it have intermintant problems.
2) How old is your CAR battery and do you ever have to jump it?
3) Does it have a shock or motion sensor? (if you don't know just turn it on and bang the car with you fist and see if it sets it off).
Shock/Sound/Motion sensors
If the sensitivity is set way to high, or the sensor is broken then it will be sending a constant trigger signal to the alarm. These sensors usually have some small LED on them that turns on when triggered (much like a home motion sensor). So if your alarm has passive arming then it will wait to arm until the sensor trigger has stopped/cleared before activating.
3) The vehicles battery drops below 9volts or so the alarm will not have the required power to operate and will be unstable. Once power has been restored in this case the alarm will go off...