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

Andre Klein·Peter Spreij
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Abstract

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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Andre Klein, Peter Spreij. 2005-05-11. The Bezoutian and Fisher's information matrix of an ARMA process. https://doi.org/10.1016/j.laa.2006.02.016

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