Common Factors and Specific Factors

Chen, Pu (2012): Common Factors and Specific Factors.

Abstract

In this paper we study factor models for security returns on financial markets, where some pervasive factors are common across all securities and other pervasive factors prevail only within some groups of securities but not in others. This kind of structured factors allow a more nuanced analysis of determinants of the security returns, in particular, they allow to study clustering structures in security returns as well as their determinants. The clustering structure provides a natural way to group the securities and to interpret common factors and group-specific factors. We give conditions under which the common factor space and the group-specific factor spaces can be identified, and propose an effective procedure to estimate the unobservable structure in the factor space. Concretely, the procedure will determine the unknown number of groups, endogenously classify securities into groups, determine the number of common factors across all groups as well as the number of group-specific factors in each group, and estimate the common factors and the group-specific factors. The estimated factor structure will provides a more meaningful interpretation of the estimated factors in practical applications.

• Item Type: MPRA Paper
• Language: English
• Keywords: Factor Models; Generalized Principal Component Analysis; Model Selection, Multiset Canonical Correlation
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Bai, J. (2003). Inference on factor models of large dimensions. Econometrica, 71:135–172.

Bai, J. and Ng, S. (2002). Determing the number of factors in approximate factor models. Econometrica, 70:191–221.

Boivin, J. and Ng, S. (2006). Are more data always better for factor analysis? Journal of Econometrics, 132:169–194.

Campell, J. Y., Lo, A. W., and Mackenlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press, 1st edition.

Chen, P. (2010). A grouped factor model. Mimeo, Melbourne University, Faculty of Business and Economics.

Fama, E. and French, K. (1993). Common risk in the returns on stocks and bonds. Journal of Financial Economics, 33:3–56.

Flury, B. (1984). Common principal components in groups. Journal of the American Statistical Association, 79:892–898.

— (1987). Two generalizations of the common principal component model. Biometrika, 62:59–69.

Goyal, A., Perignon, C., and Villa, C. (2008). How common are common return factors across nyse and nasdaq? Journal of Financial Economics, 90:252– 271.

Hasan, M. A. (June 2009). Stable algorithm for multiset canonical correlations analysis. 2009 American Control Conference, page 1280.

Jackson, J. E. (2005). Promax rotation. Encyclopedia of Biostatistics, Second Edition.

Johansen, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. Prentice-Hall International, 3rd edition.

Kaiser, H. F. (1958). The varimax ctiterion for analytic rotation in factor analysis. Psychometrika, 23:187–200.

Krzanowski, W. J. (1979). Between-groups comparison of principal components. Journal of the American Statistical Association, 74:703–707.

L., H. S. and Rouwenborst, K. G. (1994). Does industry structure explain the benefits on international diversification? Journal of Financial Economics, 36:3–7.

Nielsen, A. A. (2002). Multiset canonical correlations analysis and multispectral, truly multitemporal remote sensing data. IEEE Transactions On Image Processing, 11 No. 3:293–305.

Nishi, R. (1984). Asymptotical properties of criteria for selection of variables in multiple regression. Ann. Statist., 12:758–765.

Ross, S. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13:341–360.

Schott, J. (1999). Partial common principal component subspaces. Biometrika, 86:899–908.

Truhar, N. (2000). Relative perturbation theory for matrix spectral decompositions. UNIVERSITY OF ZAGREB DEPARTMENT OF MATHEMATICS.