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On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

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  • Bing-Yi Jing
  • Zhi Liu
  • Xin-Bing Kong

Abstract

In this article, we propose a nonparametric procedure to estimate the integrated volatility of an Itô semimartingale in the presence of jumps and microstructure noise. The estimator is based on a combination of the preaveraging method and threshold technique, which serves to remove microstructure noise and jumps, respectively. The estimator is shown to work for both finite and infinite activity jumps. Furthermore, asymptotic properties of the proposed estimator, such as consistency and a central limit theorem, are established. Simulations results are given to evaluate the performance of the proposed method in comparison with other alternative methods.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:3:p:457-467
    DOI: 10.1080/07350015.2014.906350
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    Cited by:

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    5. 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.
    6. Li, Shaoyu & Zheng, Tingguo, 2017. "Modeling spot rate using a realized stochastic volatility model with level effect and dynamic drift☆," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 200-221.
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    8. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    9. Liu, Zhi & Kong, Xin-Bing & Jing, Bing-Yi, 2018. "Estimating the integrated volatility using high-frequency data with zero durations," Journal of Econometrics, Elsevier, vol. 204(1), pages 18-32.
    10. Christensen, Kim & Thyrsgaard, Martin & Veliyev, Bezirgen, 2019. "The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing," Journal of Econometrics, Elsevier, vol. 212(2), pages 556-583.
    11. Hwang, Eunju & Shin, Dong Wan, 2014. "A bootstrap test for jumps in financial economics," Economics Letters, Elsevier, vol. 125(1), pages 74-78.
    12. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.
    13. Qiang Liu & Zhi Liu & Chuanhai Zhang, 2020. "Heteroscedasticity test of high-frequency data with jumps and microstructure noise," Papers 2010.07659, arXiv.org.
    14. Yu, Chao & Fang, Yue & Zhao, Xujie & Zhang, Bo, 2013. "Kernel filtering of spot volatility in presence of Lévy jumps and market microstructure noise," MPRA Paper 63293, University Library of Munich, Germany, revised 10 Mar 2014.
    15. Jacod, Jean & Li, Yingying & Zheng, Xinghua, 2019. "Estimating the integrated volatility with tick observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 80-100.
    16. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    17. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    18. Fu, Jin-Yu & Lin, Jin-Guan & Hao, Hong-Xia, 2023. "Volatility analysis for the GARCH–Itô–Jumps model based on high-frequency and low-frequency financial data," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1698-1712.
    19. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    20. Zhang, Chuanhai & Liu, Zhi & Liu, Qiang, 2021. "Jumps at ultra-high frequency: Evidence from the Chinese stock market," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    21. Yiqi Liu & Qiang Liu & Zhi Liu & Deng Ding, 2017. "Determining the integrated volatility via limit order books with multiple records," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1697-1714, November.
    22. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.

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