  In this paper we derive some properties of the Bezout matrix and relate the
Fisher information matrix for a stationary ARMA process to the Bezoutian. Some
properties are explained via realizations in state space form of the
derivatives of the white noise process with respect to the parameters. A
factorization of the Fisher information matrix as a product in factors which
involve the Bezout matrix of the associated AR and MA polynomials is derived.
  From this factorization we can characterize singularity of the Fisher
information matrix.
