High-dimensional covariance matrix estimation in approximate factor models

Details High-dimensional covariance matrix estimation in approximate factor models High-dimensional covariance matrix estimation in approximate factor models

2011-05-21

arxiv.org/abs/1105.4292v3

Annals of Statistics 2011, Vol. 39, No. 6, 3320-3356

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/11-AOS944 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS944

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 the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672--684], 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.

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