I must confess that i am a fan of the mysterious and unexplained but i was a little skeptical at the idea of a haunted swing but after viewing the video below there is definitely something hinky going on the way that it swings by itself.

The other thing that crossed my mind was that maybe its a hoax but a crowd of people can be seen watching and hoaxes are best done with no audience since the more people that know a secret (like you made a hoax about a swing), the less likely it is to remain a secret