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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.

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  • José Casals Carro & Alfredo García-Hiernaux & Miguel Jerez, 2010. "From general State-Space to VARMAX models," Documentos de Trabajo del ICAE 1002, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  • Handle: RePEc:ucm:doicae:1002

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. Lutkepohl, Helmut & Poskitt, D S, 1996. "Specification of Echelon-Form VARMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 69-79, January.
    5. 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.
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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. repec:kuk:journl:v:50:y:2017:i:3:p:299-336 is not listed on IDEAS
    3. Stefan Kerbl & Michael Sigmund, 2011. "What Drives Aggregate Credit Risk?," Financial Stability Report, Oesterreichische Nationalbank (Austrian Central Bank), issue 22, pages 72-87.
    4. Dr. Michael Sigmund & Dr. Ingrid Stein, 2017. "What predicts Financial (In)Stability? A Bayesian Approach," Credit and Capital Markets, Credit and Capital Markets, vol. 50(3), pages 299-336.

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

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