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A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables
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A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables

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  • Chen, J.
  • Li, D.
  • Linton, O.

Abstract

This paper studies the estimation of large dynamic covariance matrices with multiple conditioning variables. We introduce an easy-to-implement semiparametric method to estimate each entry of the covariance matrix via model averaging marginal regression, and then apply a shrinkage technique to obtain the dynamic covariance matrix estimation. Under some regularity conditions, we derive the asymptotic properties for the proposed estimators including the uniform consistency with general convergence rates. We further consider extending our methodology to deal with the scenarios: (i) the number of conditioning variables is divergent as the sample size increases, and (ii) the large covariance matrix is conditionally sparse relative to contemporaneous market factors. We provide a simulation study that illustrates the finite-sample performance of the developed methodology. We also provide an application to financial portfolio choice from daily stock returns.

Suggested Citation

  • Chen, J. & Li, D. & Linton, O., 2018. "A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables," Cambridge Working Papers in Economics 1876, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1876
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    Cited by:

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    3. Chenlei Leng & Degui Li & Hanlin Shang & Yingcun Xia, 2024. "Covariance Function Estimation for High-Dimensional Functional Time Series with Dual Factor Structures," Papers 2401.05784, arXiv.org, revised Jan 2024.
    4. Bu, R. & Li, D. & Linton, O. & Wang, H., 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Cambridge Working Papers in Economics 2218, Faculty of Economics, University of Cambridge.
    5. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    6. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    7. Fan, Qingliang & Wu, Ruike & Yang, Yanrong & Zhong, Wei, 2024. "Time-varying minimum variance portfolio," Journal of Econometrics, Elsevier, vol. 239(2).
    8. Xuan Liang & Jiti Gao & Xiaodong Gong, 2019. "Time-Varying Coefficient Spatial Autoregressive Panel Data Model with Fixed Effects," Monash Econometrics and Business Statistics Working Papers 26/19, Monash University, Department of Econometrics and Business Statistics.
    9. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    10. Jiti Gao & Bin Peng & Yayi Yan, 2022. "A Simple Bootstrap Method for Panel Data Inferences," Monash Econometrics and Business Statistics Working Papers 7/22, Monash University, Department of Econometrics and Business Statistics.
    11. Ge, S. & Li, S. & Linton, O. B. & Liu, W. & Su, W., 2024. "Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?," Janeway Institute Working Papers 2416, Faculty of Economics, University of Cambridge.
    12. Ge, S. & Li, S. & Linton, O. B. & Liu, W. & Su, W., 2024. "Should We Augment Large Covariance Matrix Estimation with Auxiliary Network Information?," Cambridge Working Papers in Economics 2427, Faculty of Economics, University of Cambridge.
    13. 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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    More about this item

    Keywords

    Dynamic covariance matrix; MAMAR; Semiparametric estimation; Sparsity; Uniform consistency;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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