We had the exact same type of thing happen to our TV last year. We would wake up in the middle of the night to our TV going. Checked the "auto" functions and everything was off. We would also come home after shopping to find our TV was on. I was almost convinced we had a haunted TV!
Turns out that the culprit was the connections to the ground fault plug in the bathroom that also controls the outlet we were using in the living room. The wire was not securely fastened in it and evidently would jiggle loose or lose/make connection. When this happened it would turn on the TV.
I pulled it out and tightened all the connections and the ghost has disappeared. Now we can sleep peacefully all night. :) I would suggest you check your ground fault adapters for loose wires also.
Barney