Department of Statistics and Actuarial Science, Chongqing University, Chongqing, China.
We apply the object-oriented robust factor analysis R package robustfa to the 28 financial indicators of the 100 listed companies in China’s Chinese Securities Index (CSI) 100 index in the first quarter of 2013. First of all, according to the size of the data, we automatically choose a robust estimator, the robust Ogk estimator. By the Mahalanobis distances which are computed by the robust Ogk estimator, greater than the critical value, we find a total of 47 abnormal points. This paper discovers that the results of the sample correlation matrix, the rotated factor loading matrix, the contribution of the factors to the original variables, the contribution rate, the cumulative contribution rate, the screeplot of the eigenvalues of the sample correlation matrix, the scatter plot of the first two factor scores, factor scores, and the sorted scores according to factor scores etc. computed by the classical estimator and the robust Ogk estimator are quite different. Finally, we condense the 28 financial indicators to 5 factors by combining the principal component analysis method and the robust Ogk estimator: Provident fund market value factor, profit factor, market value profit rate factor, value per share factor, and asset liability factor. Finally, we sort the 5 factor scores from high to low of each factor, and also get some special stocks according to the factor scores. The robust factor analysis results provide a good basis for investors to choose the stocks.
Zhang, Y. (2014) Robust Factor Analysis and Its Applications in the CSI 100 Index. Open Journal of Social Sciences, 2, 12-18. doi: 10.4236/jss.2014.27003.
[1] Yang, H. (2013) Multivariate Statistical Analysis. Chongqing University Press, Chongqing. [2] Xue, Y. and Chen, L.P. (2009) Statistical Modeling and R Software. Tsinghua University Press, Beijing. [3] Wang, X.M. (2009) Applied Multivariate Analysis. 3rd Edition, Shanghai University of Finance and Economics Press, Shanghai. [4] Zhang, T.J., Yang, A.M. and Zhang, C.H. (2008) An Empirical Study of Operational Risk Control Model of State- Owned Commercial Banks—Based on Exploratory Factor Analysis and Confirmatory Factor Analysis Point Inspection. Journal of Chongqing University (Social Science Edition), 14, 36-43. [5] Pison, G., Rousseeuw, P.J., Filzmoser, P. and Croux, C. (2003) Robust Factor Analysis. Journal of Multivariate Analy- sis, 84, 145-172. http://dx.doi.org/10.1016/S0047-259X(02)00007-6 [6] Maronna, R.A., Martin, D. and Yohai, V. (2006) Robust Statistics: Theory and Methods. John Wiley & Son, New York. http://dx.doi.org/10.1002/0470010940 [7] Todorov, V. and Filzmoser, P. (2009) An Object-Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32, 1-47. http://www.jstatsoft.org/v32/i03/ [8] Rous-seeuw, P.J., Croux, C., Todorov, V., Ruckstuhl, A., Salibian-Barrera, M., Verbeke, T. and Maechler, M. (2013) Ro-bustbase: Basic Robust Statistics. R Package Version 0.9-10. http://CRAN.R-project.org/package=robustbase [9] Wang, J., Zamar, R., Marazzi, A., Yohai, V., Salibian-Barrera, M., Maronna, R., Zivot, E., Rocke, D., Martin, D. and Konis, K. (2013) Robust: Insightful Robust Library. R Package Version 0.4-15. http://CRAN.R-project.org/package=robust [10] Todorov, V. (2013) Rrcov: Scalable Robust Estimators with High Breakdown Point. R Package Version 1.3-4. http://CRAN.R-project.org/package=rrcov [11] Zhang, Y.Y. (2013) Robustfa: An Object Oriented Solution for Robust Factor Analysis. R Package Version 1.0-5. http://CRAN.R-project.org/package=robustfa