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State-Varying Factor Models of Large Dimensions

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  • Markus Pelger
  • Ruoxuan Xiong

Abstract

This article develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and state-varying loadings under a large cross-section and time dimension. Our estimator combines nonparametric methods with principal component analysis. We derive the rate of convergence and limiting normal distribution for the factors, loadings, and common components. In addition, we develop a statistical test for a change in the factor structure in different states. We apply the estimator to the U.S. Treasury yields and S&P500 stock returns. The systematic factor structure in treasury yields differs in times of booms and recessions as well as in periods of high market volatility. State-varying factors based on the VIX capture significantly more variation and pricing information in individual stocks than constant factor models.

Suggested Citation

  • Markus Pelger & Ruoxuan Xiong, 2022. "State-Varying Factor Models of Large Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1315-1333, June.
    • Handle: RePEc:taf:jnlbes:v:40:y:2022:i:3:p:1315-1333
    DOI: 10.1080/07350015.2021.1927744
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    3. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    4. Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    5. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    6. Yufeng Mao & Bin Peng & Mervyn J Silvapulle & Param Silvapulle & Yanrong Yang, 2021. "Decomposition of Bilateral Trade Flows Using a Three-Dimensional Panel Data Model," Monash Econometrics and Business Statistics Working Papers 7/21, Monash University, Department of Econometrics and Business Statistics.
    7. Kasper Johansson & Mehmet Giray Ogut & Markus Pelger & Thomas Schmelzer & Stephen Boyd, 2023. "A Simple Method for Predicting Covariance Matrices of Financial Returns," Papers 2305.19484, arXiv.org, revised Nov 2023.
    8. Stephen Boyd & Kasper Johansson & Ronald Kahn & Philipp Schiele & Thomas Schmelzer, 2024. "Markowitz Portfolio Construction at Seventy," Papers 2401.05080, arXiv.org.
    9. Yufeng Mao & Bin Peng & Mervyn Silvapulle & Param Silvapulle & Yanrong Yang, 2021. "Decomposition of Bilateral Trade Flows Using a Three-Dimensional Panel Data Model," Papers 2101.06805, arXiv.org.
    10. Luyang Chen & Markus Pelger & Jason Zhu, 2024. "Deep Learning in Asset Pricing," Management Science, INFORMS, vol. 70(2), pages 714-750, February.
    11. Xiong, Ruoxuan & Pelger, Markus, 2023. "Large dimensional latent factor modeling with missing observations and applications to causal inference," Journal of Econometrics, Elsevier, vol. 233(1), pages 271-301.
    12. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    13. Xialu Liu & John Guerard & Rong Chen & Ruey Tsay, 2024. "Improving Estimation of Portfolio Risk Using New Statistical Factors," Papers 2409.17182, arXiv.org.
    14. Pelger, Markus, 2019. "Large-dimensional factor modeling based on high-frequency observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 23-42.

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