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Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models

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  • Matteo Barigozzi
  • Matteo Luciani

Abstract

This paper considers estimation of large dynamic factor models with common and idiosyncratic trends by means of the Expectation Maximization algorithm, implemented jointly with the Kalman smoother. We show that, as the cross-sectional dimension $n$ and the sample size $T$ diverge to infinity, the common component for a given unit estimated at a given point in time is $\min(\sqrt n,\sqrt T)$-consistent. The case of local levels and/or local linear trends trends is also considered. By means of a MonteCarlo simulation exercise, we compare our approach with estimators based on principal component analysis.

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  • Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models," Papers 1910.09841, arXiv.org.
    • Handle: RePEc:arx:papers:1910.09841
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Matteo Barigozzi & Angelo Cuzzola & Marco Grazzi & Daniele Moschella, 2025. "Factoring in the Micro: A Transaction‐Level Dynamic Factor Approach to the Decomposition of Export Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 87(1), pages 155-184, February.
    2. 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.
    3. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    4. Barigozzi, Matteo & Massacci, Daniele, 2025. "Modelling large dimensional datasets with Markov switching factor models," Journal of Econometrics, Elsevier, vol. 247(C).
    5. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    6. Paolo Andreini & Cosimo Izzo & Giovanni Ricco, 2020. "Deep Dynamic Factor Models," Papers 2007.11887, arXiv.org, revised May 2023.
    7. Lucchetti, Riccardo & Venetis, Ioannis A., 2020. "A replication of "A quasi-maximum likelihood approach for large, approximate dynamic factor models" (Review of Economics and Statistics, 2012)," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 14, pages 1-14.
    8. Hie Joo Ahn & Matteo Luciani, 2021. "Relative prices and pure inflation since the mid-1990s," Finance and Economics Discussion Series 2021-069, Board of Governors of the Federal Reserve System (U.S.).
    9. Fresoli, Diego & Poncela, Pilar & Ruiz, Esther, 2023. "Ignoring cross-correlated idiosyncratic components when extracting factors in dynamic factor models," Economics Letters, Elsevier, vol. 230(C).
    10. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    11. Luke Hartigan & Michelle Wright, 2021. "Financial Conditions and Downside Risk to Economic Activity in Australia," RBA Research Discussion Papers rdp2021-03, Reserve Bank of Australia.
    12. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    13. Serena Ng & Susannah Scanlan, 2024. "Constructing high frequency economic indicators by imputation," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 1-30.
    14. Poncela, Pilar & Ruiz, Esther, 2020. "A comment on the dynamic factor model with dynamic factors," Economics Discussion Papers 2020-7, Kiel Institute for the World Economy (IfW Kiel).
    15. Matteo Barigozzi, 2023. "Asymptotic equivalence of Principal Components and Quasi Maximum Likelihood estimators in Large Approximate Factor Models," Papers 2307.09864, arXiv.org, revised Jun 2024.

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