From general State-Space to VARMAX models

  1. Casals Carro, José
  2. Garcia-Hiernaux, Alfredo
  3. Jerez Méndez, Miguel
Journal:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Year of publication: 2010

Issue: 2

Pages: 1-28

Type: Working paper

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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 specically 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 rst one computes the coecients of a standard VARMAX model under some assumptions while the second, which is more general, returns the coecients 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.

Bibliographic References

  • Aoki, M. (1990). State Space Modelling of Time Series. Springer Verlag, New York.
  • Bujosa, M., García-Ferrer, A., and Young, P. C. (2007). Linear dynamic harmonic regression. Computational Statistics and Data Analysis, 52(2):999–1024.
  • Casals, J., Jerez, M., and Sotoca, S. (2002). An exact multivariate modelbased structural decomposition. Journal of the American Statistical Association, 97(458):553–564.
  • Casals, J., Sotoca, S., and Jerez, M. (1999). A fast and stable method to compute the likelihood of time invariant state space models. Economics Letters, 65(3):329–337.
  • Dickinson, B., Morf, M., and Kailath, T. (1974). Canonical matrix fraction and state space descriptions for deterministic and stochastic linear systems. IEEE Transactions on Automatic Control, AC-19:656–667.
  • Hannan, E. J. and Deistler, M. (1988). The Statistical Theory of Linear Systems. John Wiley, New York.
  • Harvey, A. and Trimbur, T. (2008). Trend estimation and the hodrick-prescott filter. Journal of the Japan Statistical Society, 38:41–49.
  • Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman Filter. Cambridge University Press.
  • Hillmer, S. and Tiao, G. (1982). An arima-model-based approach to seasonal adjustment. Journal of the American Statistical Association, 77:63–70.
  • Luenberger, D. G. (1967). Canonical forms for linear multivariate systems. IEEE Transactions on Automatic Control, AC-12:290–293.
  • Lütkepohl, H. and Poskitt, D. S. (1996). Specification of echelon form VARMA models. Journal of Business and Economic Statistics, 14(1):69–79.
  • Mélard, G., Roy, R., and Saidi, A. (2006). Exact maximum likelihood estimation of structured or unit root multivariate time series models. Computational Statistics and Data Analysis, 50,11:2958–2986.
  • Nerlove, M., Grether, D. M., and Carvalho, J. L. (1995). Analysis of Economic Time Series: A Synthesis. Academic Press, New York.
  • Quenouille, M. H. (1957). The Analysis of Multiple Time Series. Griffin, London.
  • Rosenbrock, H. H. (1970). State Space and Multivariable Theory. John Wiley, New York.
  • Tong, H. (1990). Nonlinear Time Series: A Dynamical System Approach. Oxford University Press, Oxford.
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