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Factor models with local factors — Determining the number of relevant factors
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Factor models with local factors — Determining the number of relevant factors

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  • Freyaldenhoven, Simon

Abstract

We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We derive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. We then introduce a new class of estimators to determine the number of those relevant factors. Unlike existing estimators, our estimators use not only the eigenvalues of the covariance matrix, but also its eigenvectors. We find that incorporating partial sums of the eigenvectors into our estimators leads to significant gains in performance in simulations.

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  • Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    • Handle: RePEc:eee:econom:v:229:y:2022:i:1:p:80-102
    DOI: 10.1016/j.jeconom.2021.04.006
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    Cited by:

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    2. Bai, Jushan & Ng, Serena, 2023. "Approximate factor models with weaker loadings," Journal of Econometrics, Elsevier, vol. 235(2), pages 1893-1916.
    3. Natalia Bailey & George Kapetanios & M. Hashem Pesaran, 2021. "Measurement of factor strength: Theory and practice," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 587-613, August.
    4. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org.
    5. Saman Banafti & Tae-Hwy Lee, 2022. "Inferential Theory for Granular Instrumental Variables in High Dimensions," Working Papers 202203, University of California at Riverside, Department of Economics.
    6. Guo, Xiao & Chen, Yu & Tang, Cheng Yong, 2023. "Information criteria for latent factor models: A study on factor pervasiveness and adaptivity," Journal of Econometrics, Elsevier, vol. 233(1), pages 237-250.
    7. Jianqing Fan & Yuling Yan & Yuheng Zheng, 2024. "When can weak latent factors be statistically inferred?," Papers 2407.03616, arXiv.org, revised Sep 2024.
    8. Wanbo Lu & Guanglin Huang & Kris Boudt, 2024. "Estimation of Non-Gaussian Factors Using Higher-order Multi-cumulants in Weak Factor Models," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 24/1085, Ghent University, Faculty of Economics and Business Administration.
    9. 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.
    10. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    11. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    12. Sylvia Kaufmann & Markus Pape, 2023. "Bayesian (non-)unique sparse factor modelling," Working Papers 23.04, Swiss National Bank, Study Center Gerzensee.
    13. 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

    High-dimensional data; Factor models; Weak factors; Local factors; Sparsity;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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