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On the Existence of One-Sided Representations in the Generalised Dynamic Factor Model

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  • Philipp Gersing

Abstract

We consider the generalised dynamic factor model (GDFM) and assume that the dynamic common component is purely non-deterministic. We show that then the common shocks (and therefore the dynamic common component) can always be represented in terms of current and past observed variables. Hence, we further generalise existing results on the so called One-Sidedness problem of the GDFM. We may conclude that the existence of a one-sided representation that is causally subordinated to the observed variables is in the very nature of the GDFM and the lack of one-sidedness is an artefact of the chosen representation.

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  • Philipp Gersing, 2024. "On the Existence of One-Sided Representations in the Generalised Dynamic Factor Model," Papers 2410.18159, arXiv.org.
    • Handle: RePEc:arx:papers:2410.18159
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    1. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    4. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    5. Hallin, Marc & Lippi, Marco, 2013. "Factor models in high-dimensional time series—A time-domain approach," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2678-2695.
    6. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2004. "The generalized dynamic factor model consistency and rates," Journal of Econometrics, Elsevier, vol. 119(2), pages 231-255, April.
    7. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2015. "Dynamic factor models with infinite-dimensional factor spaces: One-sided representations," Journal of Econometrics, Elsevier, vol. 185(2), pages 359-371.
    8. Forni, Mario & Lippi, Marco, 2011. "The general dynamic factor model: One-sided representation results," Journal of Econometrics, Elsevier, vol. 163(1), pages 23-28, July.
    9. Tamás Szabados, 2022. "Regular multidimensional stationary time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 263-284, March.
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