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Robust High-Dimensional Volatility Matrix Estimation for High-Frequency Factor Model

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  • Jianqing Fan
  • Donggyu Kim

Abstract

High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Itô process with microstructural noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions for observed log-returns. These assumptions are at odd with the heavy tail phenomenon that is pandemic in financial stock returns and new procedures are needed to mitigate the influence of heavy tails. In this article, we introduce the Huber loss function with a diverging threshold to develop a robust realized volatility estimation. We show that it has the sub-Gaussian concentration around the volatility with only finite fourth moments of observed log-returns. With the proposed robust estimator as input, we further regularize it by using the principal orthogonal component thresholding (POET) procedure to estimate the large volatility matrix that admits an approximate factor structure. We establish the asymptotic theories for such low-rank plus sparse matrices. The simulation study is conducted to check the finite sample performance of the proposed estimation methods.

Suggested Citation

  • Jianqing Fan & Donggyu Kim, 2018. "Robust High-Dimensional Volatility Matrix Estimation for High-Frequency Factor Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1268-1283, July.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1268-1283
    DOI: 10.1080/01621459.2017.1340888
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    Citations

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    Cited by:

    1. Song, Xinyu & Kim, Donggyu & Yuan, Huiling & Cui, Xiangyu & Lu, Zhiping & Zhou, Yong & Wang, Yazhen, 2021. "Volatility analysis with realized GARCH-Itô models," Journal of Econometrics, Elsevier, vol. 222(1), pages 393-410.
    2. Donggyu Kim & Xinyu Song & Yazhen Wang, 2020. "Unified Discrete-Time Factor Stochastic Volatility and Continuous-Time Ito Models for Combining Inference Based on Low-Frequency and High-Frequency," Papers 2006.12039, arXiv.org.
    3. Minseog Oh & Donggyu Kim, 2021. "Effect of the U.S.--China Trade War on Stock Markets: A Financial Contagion Perspective," Papers 2111.09655, arXiv.org.
    4. Sung Hoon Choi & Donggyu Kim, 2022. "Large Volatility Matrix Analysis Using Global and National Factor Models," Papers 2208.12323, arXiv.org, revised Dec 2022.
    5. Dohyun Chun & Donggyu Kim, 2021. "State Heterogeneity Analysis of Financial Volatility Using High-Frequency Financial Data," Papers 2102.13404, arXiv.org.
    6. Sun, Yucheng & Xu, Wen & Zhang, Chuanhai, 2023. "Identifying latent factors based on high-frequency data," Journal of Econometrics, Elsevier, vol. 233(1), pages 251-270.
    7. Choi, Sung Hoon & Kim, Donggyu, 2023. "Large volatility matrix analysis using global and national factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1917-1933.
    8. Kim, Donggyu & Fan, Jianqing, 2019. "Factor GARCH-Itô models for high-frequency data with application to large volatility matrix prediction," Journal of Econometrics, Elsevier, vol. 208(2), pages 395-417.
    9. Claudiu Vințe & Marcel Ausloos, 2023. "Portfolio Volatility Estimation Relative to Stock Market Cross-Sectional Intrinsic Entropy," JRFM, MDPI, vol. 16(2), pages 1-24, February.
    10. Kim, Donggyu & Song, Xinyu & Wang, Yazhen, 2022. "Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. Fan, Jianqing & Kim, Donggyu, 2019. "Structured volatility matrix estimation for non-synchronized high-frequency financial data," Journal of Econometrics, Elsevier, vol. 209(1), pages 61-78.
    12. Donggyu Kim & Minseok Shin & Yazhen Wang, 2021. "Overnight GARCH-It\^o Volatility Models," Papers 2102.13467, arXiv.org, revised Jun 2022.
    13. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    14. Li, Y-N. & Chen, J. & Linton, O., 2021. "Estimation of Common Factors for Microstructure Noise and Efficient Price in a High-frequency Dual Factor Model," Cambridge Working Papers in Economics 2150, Faculty of Economics, University of Cambridge.
    15. Xinyu Song, 2019. "Large Volatility Matrix Prediction with High-Frequency Data," Papers 1907.01196, arXiv.org, revised Sep 2019.
    16. De Nard, Gianluca & Zhao, Zhao, 2023. "Using, taming or avoiding the factor zoo? A double-shrinkage estimator for covariance matrices," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 23-35.
    17. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2021. "Next Generation Models for Portfolio Risk Management: An Approach Using Financial Big Data," Papers 2102.12783, arXiv.org, revised Feb 2022.
    18. Donggyu Kim, 2021. "Exponential GARCH-Ito Volatility Models," Papers 2111.04267, arXiv.org.
    19. Chen, Elynn Y. & Fan, Jianqing & Zhu, Xuening, 2023. "Community network auto-regression for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1239-1256.
    20. Donggyu Kim & Minseog Oh, 2023. "Dynamic Realized Minimum Variance Portfolio Models," Papers 2310.13511, arXiv.org.

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