Do they exist?
Using the scientific method on the paranormal is pretty far fetched, because the observation is typically based on personal accounts; when applying the scientific method, one couldn't get passed the hypothesis. Just because YOU saw it, doesn't make it enough for me to believe it. ("Extraordinary claims require extraordinary evidence) Which is why the paranormal fall into the category of pseudoscience: which is a theory mistaken as scientific. Here is my failed attempt at applying parts of the scientific method to paranormal activitiy.
In parts of paranormal activity 1, when someone has had experience with the paranormal they OBSERVE a mysterious shadow, and the temperature will drop. In the Hypothesis one would conclude that spirits of ghosts drop the temperature of a room, and that shadowy figures are ghosts. One shouldn't make casual connections with an occurrence that has only occurred once. There are also multiple variables that cause a room to have cold spots, and shadows to appear. ("Correlation isn't Causation")
A theory for this hypothesis would need to foresee future paranormal events. If I use my hypothesis that shadowy figures are spirits and cause temperatures to drop, then I should be able to say that whenever a ghost or spirit is around, there will ALWAYS be a temperature drop. My hypothesis has just been proven false.
My question is still , Do the paranormal exist? As much as I would like to answer that question based on my experiences, I cannot. That's bad science.