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A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation

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  • Shaojun Guo
  • John Leigh Box
  • Wenyang Zhang

Abstract

Estimation of high-dimensional covariance matrices is an interesting and important research topic. In this article, we propose a dynamic structure and develop an estimation procedure for high-dimensional covariance matrices. Asymptotic properties are derived to justify the estimation procedure and simulation studies are conducted to demonstrate its performance when the sample size is finite. By exploring a financial application, an empirical study shows that portfolio allocation based on dynamic high-dimensional covariance matrices can significantly outperform the market from 1995 to 2014. Our proposed method also outperforms portfolio allocation based on the sample covariance matrix, the covariance matrix based on factor models, and the shrinkage estimator of covariance matrix. Supplementary materials for this article are available online.

Suggested Citation

  • Shaojun Guo & John Leigh Box & Wenyang Zhang, 2017. "A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 235-253, January.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:235-253
    DOI: 10.1080/01621459.2015.1129969
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    1. Chen, Jia & Li, Degui & Linton, Oliver, 2019. "A new semiparametric estimation approach for large dynamic covariance matrices with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 212(1), pages 155-176.
    2. da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    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.
    4. Nadège Ribau-Peltre & Pascal Damel & An Lethi, 2018. "A methodology to avoid over-diversification of funds of equity funds An implementation case study for equity funds of funds in bull markets," Post-Print hal-03027770, HAL.
    5. Li, Jialiang & Zhang, Wenyang & Kong, Efang, 2018. "Factor models for asset returns based on transformed factors," Journal of Econometrics, Elsevier, vol. 207(2), pages 432-448.
    6. Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.

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