Before revision:  We obtain necessary and sufficient conditions for the existence of I(1) solutions to a given autoregressive law of motion generalizing the Johansen I(1) condition, and a characterization of such solutions. To accomplish this we obtain necessary and sufficient conditions for a pole in the inverse of a holomorphic index-zero Fredholm operator pencil to be simple, and a formula for its residue.
After revision:  We first obtain a range of necessary and sufficient conditions for a pole in the inverse of a holomorphic index-zero Fredholm operator pencil to be simple, and a formula for its residue.