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A spectral EM algorithm for dynamic factor models

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  • Fiorentini, Gabriele
  • Galesi, Alessandro
  • Sentana, Enrique

Abstract

We make two complementary contributions to efficiently estimate dynamic factor models: a frequency domain EM algorithm and a swift iterated indirect inference procedure for ARMA models with no asymptotic efficiency loss for any finite number of iterations. Although our procedures can estimate such models with many series without good initial values, near the optimum we recommend switching to a gradient method that analytically computes spectral scores using the EM principle. We successfully employ our methods to construct an index that captures the common movements of US sectoral employment growth rates, which we compare to the indices obtained by semiparametric methods.

Suggested Citation

  • Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:1:p:249-279
    DOI: 10.1016/j.jeconom.2018.03.013
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    Cited by:

    1. Gabriele Fiorentini & Alessandro Galesi & Enrique Sentana, 2016. "Fast ML Estimation of Dynamic Bifactor Models: An Application to European Inflation," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 215-282, Emerald Group Publishing Limited.
    2. Gabriele Fiorentini & Enrique Sentana, 2016. "Neglected serial correlation tests in UCARIMA models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 121-178, March.
    3. Martín Almuzara & Gabriele Fiorentini & Enrique Sentana, 2023. "Aggregate Output Measurements: A Common Trend Approach," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 3-33, Emerald Group Publishing Limited.
    4. 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.
    5. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    6. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    7. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    8. Dickhaus, Thorsten & Sirotko-Sibirskaya, Natalia, 2019. "Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 30-46.
    9. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," PSE Working Papers halshs-02262202, HAL.
    10. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    11. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    12. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised Dec 2023.
    13. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers halshs-02262202, HAL.
    14. Riccardo (Jack) Lucchetti & Ioannis A. Venetis, 2019. "Dynamic Factor Models in gretl. The DFM package," gretl working papers 7, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    15. Michael Creel, 2021. "Inference Using Simulated Neural Moments," Econometrics, MDPI, vol. 9(4), pages 1-15, September.
    16. Alonso Fernández, Andrés Modesto & Bastos, Guadalupe & García-Martos, Carolina, 2017. "BIAS correction for dynamic factor models," DES - Working Papers. Statistics and Econometrics. WS 24029, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. 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 Feb 2022.

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    More about this item

    Keywords

    Indirect inference; Kalman filter; Sectoral employment; Spectral maximum likelihood; Wiener–Kolmogorov filter;
    All these keywords.

    JEL classification:

    • 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
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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