You need to tell her that so as long as her 'ghost friend' is causing mischief, she will have to take responsibility for her. That includes accepting any and all punishments or sanctions that you feel are appropriate for what she does.
tl;dr you need to remove all incentive of having an imaginary friend like that and get her to take responsibility for her actions.
Be careful if you do try to find out if there really is a ghost. Because if there really is a ghost then what? At least pretending it really is an imaginary fiend you don't have to deal with the ghost.
Oh and let her watch "Paranormal Activity" that might fix her.
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