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Rank regularized estimation of approximate factor models

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  • Bai, Jushan
  • Ng, Serena

Abstract

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of removing the contribution of factors associated with small singular values from the common component. The method has been used in the machine learning literature to recover low-rank matrices. We study the procedure from the perspective of estimating an approximate factor model. Under the rank-constraint, the common component is estimated by the space spanned by factors whose singular values exceed a threshold. The desire for minimum rank and parsimony lead to a data-dependent penalty for selecting the number of factors. The new criterion is more conservative than the existing deterministic penalties and is appropriate when the nominal number of factors is inflated by the presence of weak factors or large measurement noise. We provide asymptotic results that can be used to test economic hypotheses.

Suggested Citation

  • Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    • Handle: RePEc:eee:econom:v:212:y:2019:i:1:p:78-96
    DOI: 10.1016/j.jeconom.2019.04.021
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    Cited by:

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    2. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    3. Horváth, Lajos & Liu, Zhenya & Rice, Gregory & Wang, Shixuan, 2020. "A functional time series analysis of forward curves derived from commodity futures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 646-665.
    4. Jie Wei & Yonghui Zhang, 2023. "Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?," Papers 2305.05934, arXiv.org, revised Nov 2024.
    5. Jin, Sainan & Miao, Ke & Su, Liangjun, 2021. "On factor models with random missing: EM estimation, inference, and cross validation," Journal of Econometrics, Elsevier, vol. 222(1), pages 745-777.
    6. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    7. 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.
    8. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    9. Liang Chen & Juan J. Dolado & Jesús Gonzalo, 2021. "Quantile Factor Models," Econometrica, Econometric Society, vol. 89(2), pages 875-910, March.
    10. Wang, Yiren & Phillips, Peter C.B. & Su, Liangjun, 2024. "Panel data models with time-varying latent group structures," Journal of Econometrics, Elsevier, vol. 240(1).
    11. Jungjun Choi & Ming Yuan, 2024. "High Dimensional Factor Analysis with Weak Factors," Papers 2402.05789, arXiv.org.
    12. Hörmann, Siegfried & Jammoul, Fatima, 2022. "Consistently recovering the signal from noisy functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    13. Freyaldenhoven, Simon, 2022. "Factor models with local factors — Determining the number of relevant factors," Journal of Econometrics, Elsevier, vol. 229(1), pages 80-102.
    14. Joaqui-Barandica, Orlando & Manotas-Duque, Diego F. & Uribe, Jorge M., 2022. "Commonality, macroeconomic factors and banking profitability," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    15. Rishab Guha & Serena Ng, 2019. "A Machine Learning Analysis of Seasonal and Cyclical Sales in Weekly Scanner Data," NBER Chapters, in: Big Data for Twenty-First-Century Economic Statistics, pages 403-436, National Bureau of Economic Research, Inc.
    16. Jonas Krampe & Luca Margaritella, 2021. "Factor Models with Sparse VAR Idiosyncratic Components," Papers 2112.07149, arXiv.org, revised May 2022.
    17. Difang Huang & Ying Liang & Boyao Wu & Yanyi Ye, 2024. "Estimating the Impact of Social Distance Policy in Mitigating COVID-19 Spread with Factor-Based Imputation Approach," Papers 2405.12180, arXiv.org.
    18. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson & Yaping Wang, 2024. "Performance of Empirical Risk Minimization For Principal Component Regression," Papers 2409.03606, arXiv.org, revised Sep 2024.
    19. Yiren Wang & Liangjun Su & Yichong Zhang, 2022. "Low-rank Panel Quantile Regression: Estimation and Inference," Papers 2210.11062, arXiv.org.
    20. Farnè, Matteo & Montanari, Angela, 2024. "Large factor model estimation by nuclear norm plus ℓ1 norm penalization," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    21. Serena Ng & Susannah Scanlan, 2023. "Constructing High Frequency Economic Indicators by Imputation," Papers 2303.01863, arXiv.org, revised Oct 2023.
    22. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    23. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

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    More about this item

    Keywords

    Singular-value thresholding; Robust principal components; Minimum-rank; Low rank decomposition; Nuclear-norm minimization;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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