Moving a parallax background automatically without moving the camera

Hello everyone !

I'm working on my second project, which is a little vertical space shooter. I've read some tutorials and implemented a parallax feature so that the different elements of the background move to different speeds. The thing is that I'd like my camera to not move, and simply let the ship stay within the camera borders.

My actual parallax system is tied to camera movement, so moving the camera will move the background, but I'd actually like to simply let the background move vertically and repeatedly without being tied to the camera, since it wont move. (maybe using looping animations ?) I don't know if I'm clear enough, let me know if you want more informations or maybe screenshots. :D