From general State-Space to VARMAX models
Fixed coecients State-Space and VARMAX models are equivalent, meaning that they are able to represent the same linear dynamics, being indistinguishable in terms of overall fit. However, each representation can be specifically adequate for certain uses, so it is relevant to be able to choose between them. To this end, we propose two algorithms to go from general State-Space models to VARMAX forms. The first one computes the coeficients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coeficients of a VARMAX echelon. These procedures supplement the results already available in the literature allowing one to obtain the State-Space model matrices corresponding to any VARMAX. The paper also discusses some applications of these procedures by solving several theoretical and practical problems.
|Date of creation:||2010|
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- Lutkepohl, Helmut & Poskitt, D S, 1996.
"Specification of Echelon-Form VARMA Models,"
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- Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December.
- Bujosa, Marcos & Garcia-Ferrer, Antonio & Young, Peter C., 2007. "Linear dynamic harmonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 999-1024, October.
- Guy Melard & Roch Roy & Abdessamad Saidi, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," ULB Institutional Repository 2013/13754, ULB -- Universite Libre de Bruxelles.
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