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Nonlinear shrinkage estimation of large integrated covariance matrices

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  • Clifford Lam
  • Phoenix Feng
  • Charlie Hu

Abstract

SummaryIntegrated covariance matrices arise in intraday models of asset returns, which allow volatility to change over the trading day. When the number of assets is large, the natural estimator of such a matrix suffers from bias due to extreme eigenvalues. We introduce a novel nonlinear shrinkage estimator for the integrated covariance matrix which shrinks the extreme eigenvalues of a realized covariance matrix back to an acceptable level, and enjoys a certain asymptotic efficiency when the number of assets is of the same order as the number of data points. Novel maximum exposure and actual risk bounds are derived when our estimator is used in constructing the minimum variance portfolio. In simulations and a real-data analysis, our estimator performs favourably in comparison with other methods.

Suggested Citation

  • Clifford Lam & Phoenix Feng & Charlie Hu, 2017. "Nonlinear shrinkage estimation of large integrated covariance matrices," Biometrika, Biometrika Trust, vol. 104(2), pages 481-488.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:2:p:481-488.
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    References listed on IDEAS

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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    4. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    5. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    6. Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 412-428, March.
    7. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    8. Mohsen Pourahmadi, 2007. "Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance--Correlation Parameters," Biometrika, Biometrika Trust, vol. 94(4), pages 1006-1013.
    9. Abadir, Karim M. & Distaso, Walter & Žikeš, Filip, 2014. "Design-free estimation of variance matrices," Journal of Econometrics, Elsevier, vol. 181(2), pages 165-180.
    10. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    11. Elena Asparouhova & Hendrik Bessembinder & Ivalina Kalcheva, 2013. "Noisy Prices and Inference Regarding Returns," Journal of Finance, American Finance Association, vol. 68(2), pages 665-714, April.
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    Cited by:

    1. Liu, Cheng & Wang, Moming & Xia, Ningning, 2022. "Design-free estimation of integrated covariance matrices for high-frequency data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Chang, Jinyuan & Hu, Qiao & Liu, Cheng & Tang, Cheng Yong, 2024. "Optimal covariance matrix estimation for high-dimensional noise in high-frequency data," Journal of Econometrics, Elsevier, vol. 239(2).
    3. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.

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