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Estimating High Dimensional Covariance Matrices and its Applications

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Author Info

  • Jushan Bai

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

  • Shuzhong Shi

    (Department of Finance, Guanghua School of Management)

Abstract

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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Bibliographic Info

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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Related research

Keywords: Factor analysis; Principal components; Singular value decomposition; Random matrix theory; Empirical Bayes; Shrinkage method; Optimal portfolios; CAPM; APT; GMM;

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References

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Citations

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Cited by:
  1. Tatsuya Kubokawa & Muni S. Srivastava, 2013. "Optimal Ridge-type Estimators of Covariance Matrix in High Dimension," CIRJE F-Series CIRJE-F-906, CIRJE, Faculty of Economics, University of Tokyo.
  2. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix," Papers 1308.0931, arXiv.org, revised Mar 2014.
  3. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2014. "Estimation of the Global Minimum Variance Portfolio in High Dimensions," Papers 1406.0437, arXiv.org.
  4. Tatsuya Kubokawa & Akira Inoue, 2012. "Estimation of Covariance and Precision Matrices in High Dimension," CIRJE F-Series CIRJE-F-855, CIRJE, Faculty of Economics, University of Tokyo.
  5. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix," Papers 1308.2608, arXiv.org, revised Jun 2014.

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