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Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

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Abstract

We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both n and T diverge to infinity: (i) the estimated loadings are \\sqrt{T}-consistent and asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are \\sqrt{n}-consistent and asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough.

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  • Matteo Barigozzi & Matteo Luciani, 2024. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Finance and Economics Discussion Series 2024-086, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:2024-86
    DOI: 10.17016/FEDS.2024.086
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    Cited by:

    1. Danilo Cascaldi-Garcia & Matteo Luciani & Michele Modugno, 2023. "Lessons from Nowcasting GDP across the World," International Finance Discussion Papers 1385, Board of Governors of the Federal Reserve System (U.S.).
    2. 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.).
    3. Linton, O. B. & Tang, H. & Wu, J., 2022. "A Structural Dynamic Factor Model for Daily Global Stock Market Returns," Cambridge Working Papers in Economics 2237, Faculty of Economics, University of Cambridge.
    4. 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).
    5. 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.
    6. Danilo Cascaldi-Garcia & Matteo Luciani & Michele Modugno, 2024. "Lessons from nowcasting GDP across the world," Chapters, in: Michael P. Clements & Ana Beatriz Galvão (ed.), Handbook of Research Methods and Applications in Macroeconomic Forecasting, chapter 8, pages 187-217, Edward Elgar Publishing.
    7. Junfan Mao & Zhigen Gao & Bing-Yi Jing & Jianhua Guo, 2024. "On the statistical analysis of high-dimensional factor models," Statistical Papers, Springer, vol. 65(8), pages 4991-5019, October.
    8. Linton, O. B. & Tang, H. & Wu, J., 2022. "A Structural Dynamic Factor Model for Daily Global Stock Market Returns," Cambridge Working Papers in Economics camjip:2214, Faculty of Economics, University of Cambridge.
    9. Filippo Pellegrino, 2021. "Factor-augmented tree ensembles," Papers 2111.14000, arXiv.org, revised Jun 2023.
    10. Linton, O. B. & Tang, H. & Wu, J., 2022. "A Structural Dynamic Factor Model for Daily Global Stock Market Returns," Janeway Institute Working Papers camjip:2214, Faculty of Economics, University of Cambridge.
    11. Diego Fresoli & Pilar Poncela & Esther Ruiz, 2024. "Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors," Papers 2407.06883, arXiv.org.

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    More about this item

    Keywords

    Approximate Dynamic Factor Model; Expectation Maximization Algorithm; Kalman Smoother; Quasi Maximum Likelihood;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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