| The problem with situations like this is trying to determine what the exact truth is, and what falsehoods things might be telling us; still, it's a possibility though, and in that case you might want to consider carefully. Had the ghost simply moved in after you, you could've asked or demanded it to leave, and chances are fairly big it would listen. However since it was most likely there before you I doubt this is the case.
In that case it's all up to you on how to deal with it? Do you want to get rid of it, send it on to where it should normally go? You can either perform a ritual, part of which involves cleansing the house/basement with incense, or try to figure out the basement's history... learn the origin of your ghost?
Another option is to accept its presense, so that it might accept yours, both as part of the house, there to stay with no intention of leaving or bothering the other.
Keep in mind that a ghost is no more than that: a spirit, a lingering presense of something long since gone without physical form..and how can something without form harm us? They can not, as long as you believe they can not - they can only harm you if you allow them to, if you give them that access to you that they need... - but that is something you need to learn to deal with yourself.
Good luck! | 
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