could be a weak battery or lose wire, i have an alarm on my chrysler and it goes off so to speak for no reason but it is more of an alert rather than the alarm going off, if i were you i would just take it back to where it was bought and installed and have them take a look at it, it should have a warranty and if your alarm poeple are like mine you should be able to pop in on them and have it looked it without any hassle.
that happend with my car just take it to the dealer or whomever installed your alarm some times the wires cross or disconnect. No biggie it should not cost you any thing. Also make sure you dont need new battries in your key fab if the batteries are low the remote can be sending mixed messages.
i dont think the alarms deter the jackers. however, a security system that wont let the car be started without a key is a pretty good deterent. maybe some day in the future they will design an alarm that automatically calls the police if the car is tampered with.
The manual offers a more involved experience. If you are a car person you will be glad you got the manual.
A 370z with an automatic is just wrong.