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Robust estimation of the number of factors for the pair-elliptical factor models

Author

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  • Shuquan Yang

    (Hefei University of Technology)

  • Nengxiang Ling

    (Hefei University of Technology)

  • Yulin Gong

    (Macau University of Science and Technology)

Abstract

In this paper, we investigate the robust estimation of the number of common factors in high-dimensional factor model with pair-elliptically distributed idiosyncratic errors. Motivated by the pandemic heavy-tail distributions of financial returns, we first introduce a pair-elliptical factor model by allowing the factors and noises to follow pairwisely the joint elliptical distributions. Compared with the elliptical factor model invented in Fan et al. (Ann Stat 46:1383–1414, 2018), the pair-elliptical factor model has more richer structure with more relaxed assumptions. We propose two robust quantile-based estimators of the number of factors and obtain the asymptotic properties of the estimators under some mild conditions. Then, some simulation studies and a real data analysis are carried out to show the effectiveness of the estimators of the factor numbers.

Suggested Citation

  • Shuquan Yang & Nengxiang Ling & Yulin Gong, 2022. "Robust estimation of the number of factors for the pair-elliptical factor models," Computational Statistics, Springer, vol. 37(3), pages 1495-1522, July.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:3:d:10.1007_s00180-021-01165-5
    DOI: 10.1007/s00180-021-01165-5
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    References listed on IDEAS

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    1. H. Wang, 2012. "Factor profiled sure independence screening," Biometrika, Biometrika Trust, vol. 99(1), pages 15-28.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    4. Xinbing Kong, 2020. "A random-perturbation-based rank estimator of the number of factors," Biometrika, Biometrika Trust, vol. 107(2), pages 505-511.
    5. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    6. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    7. Liang Chen & Juan J. Dolado & Jesús Gonzalo, 2021. "Quantile Factor Models," Econometrica, Econometric Society, vol. 89(2), pages 875-910, March.
    8. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    9. Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    10. Lorenzo Trapani, 2018. "A Randomized Sequential Procedure to Determine the Number of Factors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1341-1349, July.
    11. Wu, Jianhong, 2016. "Robust determination for the number of common factors in the approximate factor models," Economics Letters, Elsevier, vol. 144(C), pages 102-106.
    12. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    13. Wu, Jianhong, 2018. "Eigenvalue difference test for the number of common factors in the approximate factor models," Economics Letters, Elsevier, vol. 169(C), pages 63-67.
    14. Xia, Qiang & Liang, Rubing & Wu, Jianhong, 2017. "Transformed contribution ratio test for the number of factors in static approximate factor models," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 235-241.
    15. Xin-Bing Kong, 2017. "On the number of common factors with high-frequency data," Biometrika, Biometrika Trust, vol. 104(2), pages 397-410.
    16. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    17. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
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