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Estimating High Dimensional Covariance Matrices and its Applications

Author

Listed:
  • 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.

Suggested Citation

  • Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    • Handle: RePEc:cuf:journl:y:2011:v:12:i:2:p:199-215
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    References listed on IDEAS

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    More about this item

    Keywords

    Factor analysis; Principal components; Singular value decomposition; Random matrix theory; Empirical Bayes; Shrinkage method; Optimal portfolios; CAPM; APT; GMM;
    All these keywords.

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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