There is proof out there of their existence such as EVP recordings, pictures of faces and shadows, and film of objects moving by themselves. What is your explanation or counter evidence?
The mind is a powerful thing, prone to hallucinations, illusions and wishful thinking.
Seeing a shadow of a person or a face on the wall is no different than seeing the figure of jesus christ on a piece of burnt toast or a dog's arse. Through millions of years of evolution, the human brain learns to recognise specific shapes, one of which being the image of a human face or human figure. Naturally, human beings will see a patch of dust and see a face in it, because the human brain is trained to see the human form in places where it isn't.
With regards to objects moving 'by themselves', I would not trust others, who are capable and likely to manufacture paranormal instances to gain attention. And even if an object moved by itself, I struggle to believe how:
Object moves by itself = OMG ghosts.
Wind, vibration, any kind of scientific duhickey, that's what I'll trust.