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Consistent estimation of time-varying loadings in high-dimensional factor models

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  • Mikkelsen, Jakob Guldbæk
  • Hillebrand, Eric
  • Urga, Giovanni

Abstract

In this paper, we develop a two-step 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. 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 linear 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

  • Mikkelsen, Jakob Guldbæk & Hillebrand, Eric & Urga, Giovanni, 2019. "Consistent estimation of time-varying loadings in high-dimensional factor models," Journal of Econometrics, Elsevier, vol. 208(2), pages 535-562.
    • Handle: RePEc:eee:econom:v:208:y:2019:i:2:p:535-562
    DOI: 10.1016/j.jeconom.2018.09.020
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    Cited by:

    1. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    2. Giovanni Urga & Fa Wang, 2022. "Estimation and Inference for High Dimensional Factor Model with Regime Switching," Papers 2205.12126, arXiv.org, revised Apr 2023.
    3. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    4. Fu, Zhonghao & Hong, Yongmiao & Wang, Xia, 2023. "Testing for structural changes in large dimensional factor models via discrete Fourier transform," Journal of Econometrics, Elsevier, vol. 233(1), pages 302-331.
    5. Urga, Giovanni & Wang, Fa, 2022. "Estimation and Inference for High Dimensional Factor Model with Regime Switching," MPRA Paper 117012, University Library of Munich, Germany, revised 10 Apr 2023.
    6. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    7. Eric Hillebrand & Jakob Mikkelsen & Lars Spreng & Giovanni Urga, 2020. "Exchange Rates and Macroeconomic Fundamentals: Evidence of Instabilities from Time-Varying Factor Loadings," CREATES Research Papers 2020-19, Department of Economics and Business Economics, Aarhus University.
    8. Urga, Giovanni & Wang, Fa, 2024. "Estimation and inference for high dimensional factor model with regime switching," Journal of Econometrics, Elsevier, vol. 241(2).

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