Welcome to the site. Is the cat in your avatar the one who won't go in the basement?
Sorry, I wasn't clear, I should just speak for myself, but Holmes is the first person who made me think of ghosts.
Since the material answers are eliminated, I'm with Holmes the improbable -that there are ghosts -- is what you're left with. In Ireland, and in the mountains, people often leave dishes of milk for the ghosts. However, I'd only do this in cold weather.
Here's a thought and it's an important one. Have you had electricians out to check your basement? Cats can hear electricity in the wires and it's possible something's off with that. The last time I thought I had ghosts -- a basement light flickering -- it turned out to be a short that was on the verge of sparking into flame. I was glad I called the electrician first.