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Maximum Likelihood Estimation of Time-Varying Loadings in High-Dimensional Factor Models

Author

Listed:
  • Jakob Guldbæk Mikkelsen

    (Aarhus University and CREATES)

  • Eric Hillebrand

    (Aarhus University and CREATES)

  • Giovanni Urga

    (Cass Business School)

Abstract
In this paper, we develop a maximum likelihood estimator of time-varying loadings in high-dimensional factor models. We specify the loadings to evolve as stationary vector autoregressions (VAR) and show that consistent estimates of the loadings parameters can be obtained by a two-step maximum likelihood estimation procedure. In the first step, principal components are extracted from the data to form factor estimates. In the second step, the parameters of the loadings VARs are estimated as a set of univariate regression models with time-varying coefficients. We document the finite-sample properties of the maximum likelihood estimator through an extensive simulation study and illustrate the empirical relevance of the time-varying loadings structure using a large quarterly dataset for the US economy.

Suggested Citation

  • Jakob Guldbæk Mikkelsen & Eric Hillebrand & Giovanni Urga, 2015. "Maximum Likelihood Estimation of Time-Varying Loadings in High-Dimensional Factor Models," CREATES Research Papers 2015-61, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-61
    as

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    File URL: https://repec.econ.au.dk/repec/creates/rp/15/rp15_61.pdf
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    References listed on IDEAS

    as
    1. Pagan, Adrian, 1980. "Some identification and estimation results for regression models with stochastically varying coefficients," Journal of Econometrics, Elsevier, vol. 13(3), pages 341-363, August.
    2. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    3. Bates, Brandon J. & Plagborg-Møller, Mikkel & Stock, James H. & Watson, Mark W., 2013. "Consistent factor estimation in dynamic factor models with structural instability," Journal of Econometrics, Elsevier, vol. 177(2), pages 289-304.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    6. Breitung, Jörg & Eickmeier, Sandra, 2011. "Testing for structural breaks in dynamic factor models," Journal of Econometrics, Elsevier, vol. 163(1), pages 71-84, July.
    7. Liu, Philip & Mumtaz, Haroon & Theophilopoulou, Angeliki, 2011. "International transmission of shocks: a time-varying factor-augmented VAR approach to the open economy," Bank of England working papers 425, Bank of England.
    8. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    9. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Fu, Zhonghao & Hong, Yongmiao & Su, Liangjun & Wang, Xia, 2023. "Specification tests for time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 235(2), pages 720-744.
    2. Riccardo Borghi & Eric Hillebrand & Jakob Mikkelsen & Giovanni Urga, 2018. "The dynamics of factor loadings in the cross-section of returns," CREATES Research Papers 2018-38, Department of Economics and Business Economics, Aarhus University.
    3. Pierre Guérin & Danilo Leiva-Leon & Massimiliano Marcellino, 2020. "Markov-Switching Three-Pass Regression Filter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 285-302, April.
    4. Pierre Guérin & Danilo Leiva-Leon & Massimiliano Marcellino, 2020. "Markov-Switching Three-Pass Regression Filter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 285-302, April.
    5. Kutateladze, Varlam, 2022. "The kernel trick for nonlinear factor modeling," International Journal of Forecasting, Elsevier, vol. 38(1), pages 165-177.
    6. Varlam Kutateladze, 2021. "The Kernel Trick for Nonlinear Factor Modeling," Papers 2103.01266, arXiv.org.

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    More about this item

    Keywords

    High-dimensional factor models; dynamic factor loadings; maximum likelihood; principal components JEL classification: C33; C55; C13;
    All these keywords.

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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