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Identification of Refined ARMA Echelon Form Models for Multivariate Time Series

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  • Nsiri, Saïd
  • Roy, Roch

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

Suggested Citation

  • Nsiri, Saïd & Roy, Roch, 1996. "Identification of Refined ARMA Echelon Form Models for Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 207-231, February.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:207-231
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    Citations

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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. 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.
    3. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    4. 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.
    5. 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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