High Dimensional Covariance Matrix Estimation in Approximate Factor Models

29 Pages Posted: 23 May 2011 Last revised: 26 May 2011

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway

Martina Mincheva

Princeton University

Date Written: May 21, 2011

Abstract

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow for the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both sparsity and factor structures. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Keywords: sparse estimation, thresholding, cross-sectional correlation, common factors, idiosyncratic, seemingly unrelated regression

Suggested Citation

Fan, Jianqing and Liao, Yuan and Mincheva, Martina, High Dimensional Covariance Matrix Estimation in Approximate Factor Models (May 21, 2011). Available at SSRN: https://ssrn.com/abstract=1849266 or http://dx.doi.org/10.2139/ssrn.1849266

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Yuan Liao (Contact Author)

Rutgers, The State University of New Jersey - New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

HOME PAGE: http://rci.rutgers.edu/~yl1114

Martina Mincheva

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

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