The Bezoutian, state space realizations and Fisher's information matrix of an ARMA process
| Authors |
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| Publication date |
2006
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| Journal |
Linear Algebra and Its Applications
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| Volume | Issue number |
416 | 1
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| Pages (from-to) |
160-174
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| Number of pages |
15
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| Organisations |
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Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
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Faculty of Economics and Business (FEB) - Amsterdam School of Economics Research Institute (ASE-RI)
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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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| Document type |
Article
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| Note |
In: Special Issue devoted to the Haifa 2005 conference on matrix theory
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| Language |
English
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| Published at |
https://doi.org/10.1016/j.laa.2006.02.016
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