The Bezoutian and Fisher's information matrix of an ARMA process

Details The Bezoutian and Fisher's information matrix of an ARMA process The Bezoutian and Fisher's information matrix of an ARMA process

2005-05-11

arxiv.org/abs/math/0505224v1

Mathematics

Statistics Theory

Scientific paper

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.

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