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Non-identifiability of VMA and VARMA systems in the mixed frequency case

Author

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

Abstract

Recently, identifiability results for VAR systems in the context of mixed frequency data have been shown in a number of papers. These results have been extended to VARMA systems, where the MA order is smaller than or equal to the AR order. Here, it is shown that in the VMA case and in the VARMA case, where the MA order exceeds the AR order, results are completely different. Then, for the case, where the innovation covariance matrix is non-singular, “typically” non-identifiability occurs – not even local identifiability. This is due to the fact that, e.g., in the VMA case, as opposed to the VAR case, the not directly observed autocovariances of the output can vary “freely”. In the singular case, i.e., when the innovation covariance matrix is singular, things may be different.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecosta:v:4:y:2017:i:c:p:31-38
    DOI: 10.1016/j.ecosta.2016.11.006
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    References listed on IDEAS

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    1. Eric Ghysels & Arthur Sinko & Rossen Valkanov, 2007. "MIDAS Regressions: Further Results and New Directions," Econometric Reviews, Taylor & Francis Journals, vol. 26(1), pages 53-90.
    2. Claudia Foroni & Massimiliano Marcellino, 2013. "A survey of econometric methods for mixed-frequency data," Working Paper 2013/06, Norges Bank.
    3. Zadrozny, Peter A., 2016. "Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 438-446.
    4. Lukas Koelbl & Alexander Braumann & Elisabeth Felsenstein & Manfred Deistler, 2016. "Estimation of VAR Systems from Mixed-Frequency Data: The Stock and the Flow Case," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 43-73, Emerald Group Publishing Limited.
    5. Massimiliano Marcellino & Christian Schumacher, 2010. "Factor MIDAS for Nowcasting and Forecasting with Ragged‐Edge Data: A Model Comparison for German GDP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(4), pages 518-550, August.
    6. Anderson, Brian D.O. & Deistler, Manfred & Felsenstein, Elisabeth & Funovits, Bernd & Koelbl, Lukas & Zamani, Mohsen, 2016. "Multivariate Ar Systems And Mixed Frequency Data: G-Identifiability And Estimation," Econometric Theory, Cambridge University Press, vol. 32(4), pages 793-826, August.
    7. Chambers, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
    8. 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.
    9. Ghysels, Eric, 2016. "Macroeconomics and the reality of mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 294-314.
    10. 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. Foroni, Claudia & Marcellino, Massimiliano & Stevanović, Dalibor, 2018. "Mixed frequency models with MA components," Discussion Papers 02/2018, Deutsche Bundesbank.
    3. Ankargren, Sebastian & Jonéus, Paulina, 2021. "Simulation smoothing for nowcasting with large mixed-frequency VARs," Econometrics and Statistics, Elsevier, vol. 19(C), pages 97-113.

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