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The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case

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  • Anderson, Brian D.O.
  • Deistler, Manfred
  • Felsenstein, Elisabeth
  • Koelbl, Lukas

Abstract

This paper is concerned with the structure of multivariate AR and ARMA systems. The emphasis is on two “non-standard” cases: We deal with the structure of singular AR and ARMA systems which generate singular spectral densities and with identifiability of ARMA systems from mixed frequency data. In the mixed frequency case we show that, for the case where the MA order is smaller than or equal to the AR order, identifiability can be achieved generically. Furthermore, we demonstrate that for a pure MA system identifiability cannot be achieved. The paper generalizes the results obtained in Anderson et al. (2015) for the AR case.

Suggested Citation

  • Anderson, Brian D.O. & Deistler, Manfred & Felsenstein, Elisabeth & Koelbl, Lukas, 2016. "The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case," Journal of Econometrics, Elsevier, vol. 192(2), pages 366-373.
    • Handle: RePEc:eee:econom:v:192:y:2016:i:2:p:366-373
    DOI: 10.1016/j.jeconom.2016.02.004
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    1. Forni, Mario & Giannone, Domenico & Lippi, Marco & Reichlin, Lucrezia, 2009. "Opening The Black Box: Structural Factor Models With Large Cross Sections," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1319-1347, October.
    2. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    3. Weitian Chen & Brian D.O. Anderson & Manfred Deistler & Alexander Filler, 2011. "Solutions of Yule‐Walker equations for singular AR processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 531-538, September.
    4. de Jong, Piet & Penzer, Jeremy, 2004. "The ARMA model in state space form," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 119-125, October.
    5. Hannan, E J, 1971. "The Identification Problem for Multiple Equation Systems with Moving Average Errors," Econometrica, Econometric Society, vol. 39(5), pages 751-765, September.
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    Cited by:

    1. Philipp Gersing & Leopold Soegner & Manfred Deistler, 2022. "Retrieval from Mixed Sampling Frequency: Generic Identifiability in the Unit Root VAR," Papers 2204.05952, arXiv.org, revised Jul 2023.
    2. Majid M. Al-Sadoon & Piotr Zwiernik, 2019. "The Identification Problem for Linear Rational Expectations Models," Working Papers 1114, Barcelona School of Economics.
    3. Cimadomo, Jacopo & Giannone, Domenico & Lenza, Michele & Monti, Francesca & Sokol, Andrej, 2022. "Nowcasting with large Bayesian vector autoregressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 500-519.
    4. Marc Hallin, 2022. "Manfred Deistler and the General Dynamic Factor Model Approach to the Analysis of High-Dimensional Time Series," Working Papers ECARES 2022-30, ULB -- Universite Libre de Bruxelles.
    5. Foroni, Claudia & Marcellino, Massimiliano & Stevanović, Dalibor, 2018. "Mixed frequency models with MA components," Working Paper Series 2206, European Central Bank.
    6. Deistler, Manfred & Koelbl, Lukas & Anderson, Brian D.O., 2017. "Non-identifiability of VMA and VARMA systems in the mixed frequency case," Econometrics and Statistics, Elsevier, vol. 4(C), pages 31-38.
    7. Ankargren, Sebastian & Jonéus, Paulina, 2021. "Simulation smoothing for nowcasting with large mixed-frequency VARs," Econometrics and Statistics, Elsevier, vol. 19(C), pages 97-113.
    8. Deistler, Manfred & Wagner, Martin, 2017. "Cointegration in singular ARMA models," Economics Letters, Elsevier, vol. 155(C), pages 39-42.
    9. Lippi, Marco & Deistler, Manfred & Anderson, Brian, 2023. "High-Dimensional Dynamic Factor Models: A Selective Survey and Lines of Future Research," Econometrics and Statistics, Elsevier, vol. 26(C), pages 3-16.
    10. Siegfried Hörmann & Gilles Nisol, 2021. "Prediction of Singular VARs and an Application to Generalized Dynamic Factor Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 295-313, May.
    11. Celina Pestano-Gabino & Concepción González-Concepción & María Candelaria Gil-Fariña, 2024. "VARMA Models with Single- or Mixed-Frequency Data: New Conditions for Extended Yule–Walker Identification," Mathematics, MDPI, vol. 12(2), pages 1-15, January.

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