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From general State-Space to VARMAX models

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Abstract

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.

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File URL: http://eprints.ucm.es/11450/1/1002.pdf
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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales in its series Documentos del Instituto Complutense de Análisis Económico with number 1002.

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Length: pages 28
Date of creation: 2010
Date of revision:
Handle: RePEc:ucm:doicae:1002

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Keywords: State-Space; VARMAX models; Canonical forms; Echelon.;

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  1. Casals J. & Jerez M. & Sotoca S., 2002. "An Exact Multivariate Model-Based Structural Decomposition," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 553-564, June.
  2. D.S. Poskitt, . "Specification of echelon form VARMA models," Statistic und Oekonometrie 9305, Humboldt Universitaet Berlin.
  3. 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.
  4. 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.
  5. 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.
  6. Melard, Guy & Roy, Roch & Saidi, Abdessamad, 2006. "Exact maximum likelihood estimation of structured or unit root multivariate time series models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2958-2986, July.
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Cited by:
  1. Judith Eidenberger & Benjamin Neudorfer & Michael Sigmund & Ingrid Stein, 2013. "Quantifying Financial Stability in Austria – New Tools for Macroprudential Supervision," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 26, pages 62-81.
  2. Stefan Kerbl & Michael Sigmund, 2011. "What Drives Aggregate Credit Risk?," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 22.

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