The back up battery should changed every 5 years - if one of the detectors is tripping the alarm when it is set and there is no-one in the room/house suspect the detector for that zone is faulty.
The detector that tripped should be displayed on your keypad when you go to disarm the system after it has tripped.
A good PIR detector costs around �10 and an even better Dual Tec sensor about �20 are very easy to replace - usually the wiring is a straight swap but you will need to know what you are doing.
Back up batteries are usually to blame if it has tripped when there is a power cut.
If you need any more help let us know.
I've had trouble with wireless alarms. When the batteries in the PIR sensors start to run down, they can throw out spurious errors. Is it close to one year since you changed them (applies to wireless only systems)
does the alarm time coincide with any heating timer etc?
I seen a commerical alarm that would sound at 7am each morning and its because the heating came on at 6.30am. The big convection heaters were fan assisted which caused office plants to flutter.
As the plants were near to the sensor, the plant would "look" huge so a trip was caused.
Motion aside, sometimes sudden heating of a wet or electric heater can trip them off but thats less common.