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Identification of Refined ARMA Echelon Form Models for Multivariate Time Series

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  • Nsiri, Saïd
  • Roy, Roch
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    Abstract

    In the present article, we are interested in the identification of canonical ARMA echelon form models represented in a "refined" form. An identification procedure for such models is given by Tsay (J. Time Ser. Anal.10(1989), 357-372). This procedure is based on the theory of canonical analysis. We propose an alternative procedure which does not rely on this theory. We show initially that an examination of the linear dependency structure of the rows of the Hankel matrix of correlations, with originkin (i.e., with correlation at lagkin position (1, 1)), allows us not only to identify the Kronecker indicesn1, ..., nd, whenk=1, but also to determine the autoregressive ordersp1, ..., pd, as well as the moving average ordersq1, ..., qdof the ARMA echelon form model by settingk>1 andk

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 2 (February)
    Pages: 207-231

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:207-231

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    Related research

    Keywords: multivariate ARMA model canonical representation Kronecker indices Hankel matrix identifiability (null);

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    Cited by:
    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. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.
    3. George Athanasopoulos & D.S. Poskitt & Farshid Vahid, 2007. "Two canonical VARMA forms: Scalar component models vis-à-vis the Echelon form," Monash Econometrics and Business Statistics Working Papers 10/07, Monash University, Department of Econometrics and Business Statistics, revised May 2009.
    4. Dufour, Jean-Marie & Tessier, David, 1997. "La causalité entre la monnaie et le revenu : une analyse fondée sur un modèle VARMA-échelon," L'Actualité Economique, Société Canadienne de Science Economique, vol. 73(1), pages 351-366, mars-juin.

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