I am not sure where the real roots are. The concept of ghosts and spirits having unfinished business and sticking around shows up in a lot of places and these days it is hard to say what influenced what. In anime it is mainly of course Japanese roots which are Shinto and Buddhist, mainly Shinto. I am not sure how closely related Shinto is to other east asian beliefs.
Personnally, I am up in the air when it comes to ghosts.
I don't know weather thay are real or not.
As a Christian, who believes when we die we go to Heaven to be with God.
I wonder why they hang aroud here and haunt places.
As for unfinished business, I believe what ever business they had while alive was completed when they died.