A grouped factor model

Chen, Pu (2010): A grouped factor model.

Abstract

In this paper we present a grouped factor model that is designed to explore clustering structures in large factor models. We develop a procedure that will endogenously assign variables to groups, determine the number of groups, and estimate common factors for each group. The grouped factor model provides not only an alternative way to factor rotations in discovering orthogonal and non-orthogonal clusterings in a factor space. It offers also an effective method to explore more general clustering structures in a factor space which are invisible by factor rotations: the factor space can consist of subspaces of various dimensions that may be disjunct, orthogonal, or intersected with any angels. Hence a grouped factor model may provide a more detailed insight into data and thus also more understandable and interpretable factors.

• Item Type: MPRA Paper
• Language: English
• Keywords: Factor Models; Generalized Principal Component Analysis; Model Selection
• 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.

Connor, G. and Korajzyk, R. (1986). A test for the number of factors in an approximate factor model. Journal of Finance, 48:1263–1291.

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.

Heaton, C. and Solo, V. (2009). Grouped variable approximate factor analysis.

15th International Conference:Computing in Economics and Finance. Johnson, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. Prentice-Hall International, 3rd edition.

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

Ludvigson, S. C. and Ng, S. (2009). A factor analysis of bond risk premia. NBER Working Paper No. 15188.

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

Stock, J. H. and Watson, M. W. (2002a). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association, 97:1167–1179.

— (2002b). Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics, 20:147–162.

Vidal, R., Ma, Y., and Piazzi, J. (2004). A new gpca algorithm for clustering subspaces by fitting, differentiating and dividing polynomials. CVPR, page 510.

Vidaly, R. (2003). Generalized principal component analysis(gpca): an algebraic geometric approach to subspace clustering and motion segmentation. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy.

Vidaly, R., Ma, Y., and Sastry, S. (2003). Generalized principal component analysis (gpca). Uncertainty in Artificial Intelligence, pages 255–268.

Yang, A. Y., Rao, S., Wagner, A., Ma, Y., and Fossum, R. M. (2005). Hilbert functions and applications to the estimation of subspace arrangements. ICCV.

Yedla, M., Pathakota, S. R., and Srinivasa, T. M. (2010). Enhancing kmeans clustering algorithm with improved initial center. International Journal of Computer Science and Information Technologies, 1 (2):121–125.

Zhang, C. and Xia, S. (2009). K-means clustering algorithm with improved initial center. Proceedings of Second International Workshop on Knowledge Discovery and Data Mining, pages 790–792.