I received this morning my first ever Arnold Schwarzenegger autograph, but, although it came with a COA, I very much doubt it is authentic - I have spent a few hours searching the Net and this forum for real Arnie autographs and I must admit mine doesn't look a thing like those he did sign. Even the COA doesn't look real to me: it is probably home-made and even has a spelling mistake (futher instead of further).
I bought the autographed photo from a French eBay seller, so I suppose it might be a European forgery notwithstanding the fact that the COA is signed by someone who is supposed to be a member of the U.A.C.C.