Teehee, a bit late but that indeed isn't a Peregrine, nor is it a Cooper's Hawk. I was wondering this when looking at the footage, especially since the tail and location of the bird were so off! This is actually a Red Shouldered Hawk, and you're pretty lucky to get to see one up close. They're generally very woodland oriented birds and eat animals such as small mammals, reptiles, and sometimes even birds. These birds have peeked interest in the falconry community for a few people, especially apprentices enthralled by the idea of a bird hunter that's not as tiny as a kestrel, but generally take poor to avid game chasing and prefer the much easier prey, as you can see. Below is the only Falconer I know of to successfully hunt multiple times with his Red Shoulder, but even so he ended up having to release it.

http://virtualvideo.cc/falconry/index.html