In Paranormal Activity 3, it is either alluded to or outright stated what is actually causing the hauntings/possessions that occur in the entire series. I can't for the life of me remember if it was supposed to be a ghost, a demon, or something else. What type of entity is supposed to be causing all of the events that are going on?
From the Paranormal Activity Wiki:
The Demon is the main antagonist of the Paranormal Activity film series, the demon haunts the families of two sisters, Katie and Krisiti. The Demon is then revealed to be Toby.
ScreenRant has a summary of the entire Paranormal Activity movie trilogy in chronological order, with the connections between the films pointed out.