The Bezoutian, state space realizations and Fisher’s information matrix of an ARMA process |
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Authors: | André Klein Peter Spreij |
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Institution: | a Department of Quantitative Economics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, Netherlands b Korteweg-de Vries Institute for Mathematics, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands |
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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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Keywords: | 15A23 15A24 15A57 62M10 93B15 93B17 |
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