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The Convergence Rates of Large Volatility Matrix Estimator Based on Noise, Jumps, and Asynchronization

Author

Listed:
  • Erlin Guo

    (School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China)

  • Cuixia Li

    (School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China)

  • Fengqin Tang

    (School of Mathematics Sciences, Huaibei Normal University, Huaibei 235000, China)

Abstract

At the turn of the 21st century, the wide availability of high-frequency data aroused an increasing demand for better modeling and statistical inference. A challenging problem in statistics and econometrics is the estimation problem of the integrated volatility matrix based on high-frequency data. The existing estimators work well for diffusion processes with micro-structural noise and may get worse when jumps are considered. This paper proposes a novel estimation in the presence of jumps, micro-structural noise, and asynchronization. First, we adopt sub-sampling to synchronize the high-frequency data. Then, we use a two-time scale to realize co-volatility to handle noise. Finally, we employ the threshold parameters to remove the effect of jumps and sparsity in two steps. Both the minimax bound and the convergence rate are discussed in the paper. The estimation procedures of the heavy-tailed data will be solved in the future.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1425-:d:1098174
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    References listed on IDEAS

    as
    1. Cui-Xia Li & Jin-Yuan Chen & Zhi Liu & Bing-Yi Jing, 2014. "On Integrated Volatility of Itô Semimartingales when Sampling Times are Endogenous," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(24), pages 5263-5275, December.
    2. repec:wyi:journl:002161 is not listed on IDEAS
    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. 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.
    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. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    7. Jin, Chenfei & Tsai, Fu-Sheng & Gu, Qiuyang & Wu, Bao, 2022. "Does the porter hypothesis work well in the emission trading schema pilot? Exploring moderating effects of institutional settings," Research in International Business and Finance, Elsevier, vol. 62(C).
    8. Zhi Liu, 2017. "Jump-robust estimation of volatility with simultaneous presence of microstructure noise and multiple observations," Finance and Stochastics, Springer, vol. 21(2), pages 427-469, April.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    10. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    11. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
    12. Jonathan Brogaard & Terrence Hendershott & Ryan Riordan, 2014. "High-Frequency Trading and Price Discovery," The Review of Financial Studies, Society for Financial Studies, vol. 27(8), pages 2267-2306.
    13. Dai, Chaoxing & Lu, Kun & Xiu, Dacheng, 2019. "Knowing factors or factor loadings, or neither? Evaluating estimators of large covariance matrices with noisy and asynchronous data," Journal of Econometrics, Elsevier, vol. 208(1), pages 43-79.
    14. Bing-Yi Jing & Zhi Liu & Xin-Bing Kong, 2014. "On the Estimation of Integrated Volatility With Jumps and Microstructure Noise," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 457-467, July.
    15. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2005. "Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities," Econometrica, Econometric Society, vol. 73(1), pages 279-296, January.
    16. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    17. Kim, Donggyu & Wang, Yazhen & Zou, Jian, 2016. "Asymptotic theory for large volatility matrix estimation based on high-frequency financial data," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3527-3577.
    18. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    19. repec:hal:journl:peer-00732537 is not listed on IDEAS
    20. Cuixia Li & Erlin Guo, 2018. "Estimation of the integrated volatility using noisy high-frequency data with jumps and endogeneity," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(3), pages 521-531, February.
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