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Adaptive thresholding for large volatility matrix estimation based on high-frequency financial data

Author

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  • Kim, Donggyu
  • Kong, Xin-Bing
  • Li, Cui-Xia
  • Wang, Yazhen

Abstract

Universal thresholding methods have been developed to estimate the large sparse integrated volatility matrix of underlying assets based on high-frequency financial data. Since the integrated volatility matrix often has entries with a wide range of variability, universal thresholding estimators do not take the varying entries into consideration and may have unsatisfactory performances. This paper investigates adaptive thresholding estimation of the large integrated volatility matrix. We first construct an estimator for the asymptotic variance of the pre-averaging realized volatility estimator and then use the two estimators to develop an adaptive thresholding estimator of the large volatility matrix. It is shown that the adaptive thresholding estimator can achieve the optimal rate of convergence over the class of the sparse integrated volatility matrix when both the number of assets and sample size are allowed to go to infinity, while the universal thresholding estimator can achieve only the sub-optimal convergence rate. Also we discuss how to harness the adaptive thresholding scheme in the approximate factor model. The simulation study is conducted to check the finite sample performance of the adaptive thresholding estimators.

Suggested Citation

  • Kim, Donggyu & Kong, Xin-Bing & Li, Cui-Xia & Wang, Yazhen, 2018. "Adaptive thresholding for large volatility matrix estimation based on high-frequency financial data," Journal of Econometrics, Elsevier, vol. 203(1), pages 69-79.
    • Handle: RePEc:eee:econom:v:203:y:2018:i:1:p:69-79
    DOI: 10.1016/j.jeconom.2017.09.006
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    Citations

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    Cited by:

    1. Kong, Xin-Bing & Liu, Zhi & Zhou, Wang, 2019. "A rank test for the number of factors with high-frequency data," Journal of Econometrics, Elsevier, vol. 211(2), pages 439-460.
    2. Jiayuan Zhou & Feiyu Jiang & Ke Zhu & Wai Keung Li, 2019. "Time series models for realized covariance matrices based on the matrix-F distribution," Papers 1903.12077, arXiv.org, revised Jul 2020.
    3. 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.
    4. Erlin Guo & Cuixia Li & Fengqin Tang, 2023. "The Convergence Rates of Large Volatility Matrix Estimator Based on Noise, Jumps, and Asynchronization," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    5. Jianqing Fan & Donggyu Kim & Minseok Shin, 2024. "Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data," Working Papers 202419, University of California at Riverside, Department of Economics.
    6. Donggyu Kim, 2024. "High-Dimensional Time-Varying Coefficient Estimation," Working Papers 202416, University of California at Riverside, Department of Economics.
    7. Donggyu Kim & Minseog Oh, 2024. "Dynamic Realized Minimum Variance Portfolio Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(4), pages 1238-1249, October.
    8. Donggyu Kim & Minseog Oh, 2024. "Dynamic Realized Minimum Variance Portfolio Models," Working Papers 202421, University of California at Riverside, Department of Economics.

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    More about this item

    Keywords

    Pre-averaging realized volatility; Regularization; Sparsity; Adaptive thresholding; Diffusion; Integrated volatility;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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