My Explanation (MAJOR SPOILERS!!!)
First off, I have to say that this is possibly one of the best films in this found footage genre. The more I think about the film, the more amazed I am at the complexity of the story telling. Yes, it may not be the most original in terms of visuals and execution, but it certainly has a very original plot and plot twist at the end. Here's why I think that...
********SPOILERS START HERE********
1. With regards to the unexplained goings-on in the apartment, anyone who's seen the film knows that the doctor is full of BS. But it's a much needed BS to throw us off from the final scene, which in my opinion explains a whole lot. More on that later. The doctor was integral, the "Scully" if you will ("X-Files" shout out!).
2. From the doctor's perspective, the banging, the voices, the flying stuff, the levitation, all stem from the teenage girl's resentment towards her father. She blames him for her mother's death, as well as (seemingly) molesting her. By the doctor's own theory stated somewhere in the middle of the film, tragedy and awful events tend to leave an echo and has a desire to be discovered (the whole "the truth will always come out" idea) even through unexplained phenomena. His first theory is that the father killed the mother and molested her daughter, and those truths are trying to be discovered.
3. The doctor then changes his tune when he interrogates the father, and it's revealed that the dead mother is schizophrenic and was a horrible woman after she stopped taking her medication. After discovering his wife with another man, while their daughter was watching, he takes the kids and flees. She goes after him and crashes her car, ending up dead. This is a very important plot point that would explain my final theory.
4. After the truth of the dead wife's mental illness comes out, the doctor then theorizes that everything happening is merely a physical manifestation of the daughter's rage, and ultimately, her mental illness as inherited from the mother. Taking a cue from "X-Men", I believe that the doctor postulates that because of adolescent hormones coupled with a tragic event, the daughter is able to do all of the things they experienced in the apartment. Now, of course that's a bit of a stretch, but the doctor concludes that there is no ghost, but there certainly is something not normal going on, but it's all part of the phenomena of the mystery of the brain. And a sick brain is capable of strange things. So by the end, we are led to believe that there is no ghost activity, but rather a yet-unexplained scientific activity is to blame. Ghosts don't exist, but powerful mental abilities do.
5. Then there's the final image. Some of you have called it cheesy, but to me, it actually rebukes all of the scientific hypotheses laid out for us to believe. Then the wheels in my brain started turning and the explanation (as derived by me, not to be taken as fact) turns out to be more chilling and sinister than I thought.
6. Yes, the ghost was real. Yes, it was the dead wife. And yes, she's pissed. Pissed at her husband for abandoning her. Pissed that she's dead. And that anger led her to want the worst for her husband. And what's the worst thing you can do to a father? Make it look like he was molesting his teenage daughter. Yes, I believe that the dead mom was trying to frame the father to get him sent to jail and ruin his life. The lifting of the nightgown, the possessed daughter screaming "You know what you did! To the girl!!!", and the smirk at the end of the final possession all point to her thinking she succeeded. Only, she didn't, hence the final appearance at the end. Consider it a last ditch attempt at being heard.
I'm curious to see if anyone else came up with this conclusion.
So, like I said, I cannot say enough about how much I think this film to be one of the best films, not just in found-footage horror, but in horror in general. It's one that makes you think, instead of just handing over every plot point on a silver platter. Plus, the green strobe-light scene made me scream out loud, and I haven't done that in YEARS! Horror films don't scare me that much (I saw "The Exorcist" when I was five and just went "Meh..." Now, I think it's an amazing piece of cinema) but this one certainly did. Highly recommended!