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Some properties of the parameterization of ARMA systems with unknown order

Author

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  • Deistler, M.
  • Hannan, E. J.

Abstract

The first section of the paper introduces known theory relating to the description of the set of all ARMA structures via the concept of order, n, and the coordinatisation of all structures, M(n), of given order. The coordinates most easily used are related to the state space representation and in the first section these are related to coordinates obtained from the ARMA representation. In the second section geometric and topological properties of M(n) are considered. For example, the closure of M(n) is just the union of all M(j), j

Suggested Citation

  • Deistler, M. & Hannan, E. J., 1981. "Some properties of the parameterization of ARMA systems with unknown order," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 474-484, December.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:4:p:474-484
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    Citations

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    Cited by:

    1. Hanzon, B., 1991. "On the closure of several sets of ARMA and linear state space models with a given structure," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Jean-Marie Dufour & Tarek Jouini, 2011. "Asymptotic Distributions for Some Quasi-Efficient Estimators in Echelon VARMA Models," CIRANO Working Papers 2011s-25, CIRANO.
    3. Dufour, Jean-Marie & Jouini, Tarek, 2014. "Asymptotic distributions for quasi-efficient estimators in echelon VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 69-86.
    4. DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
    5. George Athanasopoulos & D. Poskitt & Farshid Vahid, 2012. "Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 60-83.
    6. B. Pötscher, 1985. "The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 129-150, December.

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