Hey
Initiative in Arena works roughly the same as Survival. (Don't quote me on this)
Where the base initiative is combined and spread equally with your characters. Which does explain alot.
Also, I don't think Arena uses any additional stat lines like Purification, 8th Inner Gates, etc. That can boost your Initiative. Just what your refinements are and that's it. Of course, that's me taking an educated guess. I'll look more into it later.