References
- Ahn, S. C. , and Horenstein, A. R. (2013), “Eigenvalue Ratio Test for the Number of Factors,” Econometrica , 81, 1203–1227.
- Bai, J. , and Ng, S. (2002), “Determining the Number of Factors in Approximate Factor Models,” Econometrica , 70, 191–221. DOI: https://doi.org/10.1111/1468-0262.00273.
- Bai, Z. D. , and Ding, X. (2012), “Estimation of Spiked Eigenvalues in Spiked Models,” Random Matrices: Theory and Applications , 1, 1150011. DOI: https://doi.org/10.1142/S2010326311500110.
- Baik, J. , and Silverstein, J. W. (2006), “Eigenvalues of Large Sample Covariance Matrices of Spiked Population Models,” Journal of Multivariate Analysis , 97, 1382–1408. DOI: https://doi.org/10.1016/j.jmva.2005.08.003.
- Bao, Z. G. , Pan, G. M. and Zhou, W. (2012), “Tracy-Widom law for the extreme eigenvalues of sample correlation matrices,” Electronic Journal of Probability , 17, 1–32. DOI: https://doi.org/10.1214/EJP.v17-1962.
- Cai, T. T. , Han, X. , and Pan, G. M. (2017), “Limiting Laws for Divergence Spiked Eigenvalues and Largest Non-Spiked Eigenvalue of Sample Covariance Matrices,” arXiv no. 1711.00217v2.
- Carhart, M. M. (1997), “On Persistence in Mutual Fund Performance,” The Journal of Finance , 52, 57–82. DOI: https://doi.org/10.1111/j.1540-6261.1997.tb03808.x.
- Dobriban, E. (2019), “Permutation Methods for Factor Analysis and PCA,” arXiv no. 1710.00479v3.
- Dobriban, E. , and Owen, A. B. (2019), “Deterministic Parallel Analysis: An Improved Method for Selecting Factors and Principal Components,” Journal of the Royal Statistical Society, Series B, 81, 163–183. DOI: https://doi.org/10.1111/rssb.12301.
- El Karoui, N. (2007), “On Spectral Properties of Large Dimensional Correlation Matrices and Covariance Matrices Computed From Elliptically Distributed Data,” Technical Report, Department of Statistics, University of California, Berkeley.
- Fama, E. F. , and French, K. R. (1993), “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics , 33, 3–56. DOI: https://doi.org/10.1016/0304-405X(93)90023-5.
- Fama, E. F. , and French, K. R. (2015), “A Five-Factor Asset Pricing Model,” Journal of Financial Economics , 116, 1–22.
- Fan, J. , Liao, Y. , and Mincheva, M. (2013), “Large Covariance Estimation by Thresholding Principal Orthogonal Complements,” Journal of the Royal Statistical Society, Series B, 75, 603–680. DOI: https://doi.org/10.1111/rssb.12016.
- Fan, J. , Wang, K. , Zhong, Y. , and Zhu, Z. (2020), “Robust High Dimensional Factor Models With Applications to Statistical Machine Learning,” Statistical Science (to appear).
- Fan, J. , Zhang, J. , and Yu, K. (2012), “Vast portfolio Selection With Gross-Exposure Constrains,” Journal of the American Statistical Association , 107, 592–606. DOI: https://doi.org/10.1080/01621459.2012.682825.
- Gao, J. T. , Han, X. , Pan, G. M. , and Yang, Y. R. (2017), “High-Dimensional Correlation Matrices: The Central Limit Theorem and Its Application,” Journal of the Royal Statistical Society, Series B, 79, 677–693. DOI: https://doi.org/10.1111/rssb.12189.
- Guttman, L. (1954), “Some Necessary Conditions for Common-Factor Analysis,” Psychometrika , 19, 149–161. DOI: https://doi.org/10.1007/BF02289162.
- Hallin, M. , and Liška, R. (2007), “Determining the Number of Factors in the General Dynamic Factor Model,” Journal of the American Statistical Association , 102, 603–617. DOI: https://doi.org/10.1198/016214506000001275.
- Harding, M. (2013), “Estimating the Number of Factors in Large Dimensional Factor Models,” manuscript.
- Johnson, R. A. , and Wichern, D. W. (2007), Applied Multivariate Statistical Analysis (6th ed.), New York: Prentice Hall.
- Kaiser, H. K. (1960), “The Application of Electronic Computers to Factor Analysis,” Educational and Psychological Measurement , 20, 141–151. DOI: https://doi.org/10.1177/001316446002000116.
- Kaiser, H. K. (1961), “A Note on Guttman’s Lower Bound for the Number of Common Factors,” The British Journal of Statistical Psychology , 14, 1–2.
- Kapetanios, G. (2010), “A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets,” Journal of Business & Economic Statistics , 28, 397–409.
- Kong, X. B. , Liu, Z. , and Zhou, W. (2019), “A Rank Test for the Number of Factors With High-Frequency Data,” Journal of Econometrics , 211, 439–460. DOI: https://doi.org/10.1016/j.jeconom.2019.03.004.
- Lam, C. , and Yao, Q. (2012), “Factor Modeling for High-Dimensional Time Series: Inference for the Number of Factors,” The Annals of Statistics , 40, 694–726. DOI: https://doi.org/10.1214/12-AOS970.
- Lewbel, A. (1991), “The Rank of Demand Systems: Theory and Nonparametric Estimation,” Econometrica , 59, 711–730. DOI: https://doi.org/10.2307/2938225.
- Li, H. J. , Li, Q. , and Shi, Y. T. (2017), “Determining the Number of Factors When the Number of Factors Can Increase With Sample Size,” Journal of Econometrics , 197, 76–86. DOI: https://doi.org/10.1016/j.jeconom.2016.06.003.
- Li, Z. , Wang, Q. , and Yao, J. (2017), “Identifying the Number of Factors From Singular Values of a Large Sample Auto-Covariance Matrix,” The Annals of Statistics , 45, 257–288. DOI: https://doi.org/10.1214/16-AOS1452.
- McCraken, M. W. , and Ng, S. (2017), “FRED-MD: A Monthly Database for Macroeconomic Research,” Journal of Business and Economic Statistics , 79, 677–693.
- Onatski, A. (2005), “A Formal Statistical Test for the Number of Factors in the Approximate Factor Models,” Mimeo, Columbia University, pp. 399–400.
- Onatski, A. (2009), “Testing Hypotheses About the Number of Factors in Large Factor Models,” Econometrica , 77, 1447–1479.
- Onatski, A. (2010), “Determining the Number of Factors From Empirical Distribution of Eigenvalues,” The Review of Economics and Statistics , 92, 1004–1016.
- Pan, J. Z. , and Yao, Q. W. (2008), “Modelling Multiple Time Series via Common Factors,” Biometrika , 95, 365–379. DOI: https://doi.org/10.1093/biomet/asn009.
- Su, L. J. , and Wang, X. (2017), “On Time-Varying Factor Models: Estimation and Testing,” Journal of Econometrics , 198, 84–101. DOI: https://doi.org/10.1016/j.jeconom.2016.12.004.
- Wang, H. (2012), “Factor Profiled Sure Independence Screening,” Biometrika , 99, 15–28. DOI: https://doi.org/10.1093/biomet/asr074.