I experienced this kind of problem on my Accord when I went to work abroad a couple of years back and left the Accord on the drive with the alarm on.
When I came back after a couple of months, the main battery was flat, I presume that the alarm slowly drained it flat. I recharged the battery in the correct manner with the neg terminal disconnected, and then when I reconnected the neg terminal the alarm started. I tried everything but could not get the alarm to stop. After about 20 minutes it stopped itself. So I disconnected the neg terminal and left it a couple of hours, then reconnected and the same thing happened. A week later I disconnected the neg terminal and the alarrm did not go off again. So I presume that the battery in the alarm had also gone flat, and had now recharged. Note that the main battery lasted me another 3 years, so nothing to do with that either.
In a house alarm, the alarm box has its own battery inside, else a burglar could find the main alarm control box and cut the wire to the alarm and it would not go off. Eventually, the battery in the alarm box ages and will not hold its charge, so when the mains power trips, the alarm box battery voltage drops and it starts to wail.
So if you follow all that, IMO, if your car alarm keeps going off, your main battery is old, and your alarm battery is old. My Accord is now 8 years old, but my alarm does not go off if I remove the neg terminal from the main battery. But this does not mean that all alarm batteries in all Accords will last that long.
EDIT: so what you need to do is:
1. check the condition of your main battery, and the terminals, and also the charging voltage when the engine is running, because the main battery should supply enough voltage to the alarm overnight even if the alarm battery is old.
2. replace the alarm battery (but I don't even know were the Accord's alarm is)