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Estimating High Dimensional Covariance Matrices and its Applications

  • Jushan Bai

    (Department of Economics, Columbia University
    CEMA, Central University of Finance and Economics)

  • Shuzhong Shi

    (Department of Finance, Guanghua School of Management)

Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.

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Article provided by Society for AEF in its journal Annals of Economics and Finance.

Volume (Year): 12 (2011)
Issue (Month): 2 (November)
Pages: 199-215

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Handle: RePEc:cuf:journl:y:2011:v:12:i:2:p:199-215
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