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

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  • Matteo Barigozzi
  • Matteo Luciani

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 the cross-sectional dimension, $n$, and the sample size, $T$, diverge to infinity: (i) the estimated loadings are $\sqrt T$-consistent, asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are $\sqrt n$-consistent, 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, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
  • Handle: RePEc:arx:papers:1910.03821
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    3. 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.).
    4. 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.
    5. Diego Fresoli & Pilar Poncela & Esther Ruiz, 2024. "Dealing with idiosyncratic cross-correlation when constructing confidence regions for PC factors," Papers 2407.06883, arXiv.org.
    6. 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.).
    7. 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.
    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 2237, Faculty of Economics, University of Cambridge.
    9. 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).

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    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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