Here is a plant that has been growing by our house for three years now. I took it for a weed but my wife took pity on it and kept me from pulling it out of the ground. So here we are three years later, it hasn't died or died back during the winter (so guessing no on being a weed or annual), it throws off little blooms and has grown a foot or so taller. It's pretty hardly for our summer 115 degree temps in AZ. I post a few pics of the plant, foliage, and bloom.
LOL and i thought it a weed. I thought looked like a lantana bloom but I haven't seen one grow so tall with leaves so big. My wife will be happy I was wrong
Name: Carol Santa Ana, ca Sunset zone 22, USDA zone 10 A.
In Hawaii, those are large shrubs! Here in So. Cal they will grow 4' tall and wide...and will clime a fence. I would think they would do about the same in Az.., if they don't freeze.