My personal view is that the authentic self is not impermanent. One reason I think this is that the "I" that starts a thought is the same "I" that finishes it - if otherwise would it really be a thought?
The "I" that is now trying to formulate a response to your post is using previous thoughts and experiences of the "I' that I have always been. If I started this formulation and you finished it for example would my post really qualify as an authentic thought?