IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.09759.html
   My bibliography  Save this paper

Estimation of Integrated Volatility Functionals with Kernel Spot Volatility Estimators

Author

Listed:
  • Jos'e E. Figueroa-L'opez
  • Jincheng Pang
  • Bei Wu

Abstract

For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-side kernels of unbounded support are more accurate, in this paper, an estimator using a general kernel spot volatility estimator as the plug-in is considered. A biased central limit theorem for estimating the integrated functional is established with an optimal convergence rate. Unbiased central limit theorems for estimators with proper de-biasing terms are also obtained both at the optimal convergence regime for the bandwidth and when applying undersmoothing. Our results show that one can significantly reduce the estimator's bias by adopting a general kernel instead of the standard uniform kernel. Our proposed bias-corrected estimators are found to maintain remarkable robustness against bandwidth selection in a variety of sampling frequencies and functions.

Suggested Citation

  • Jos'e E. Figueroa-L'opez & Jincheng Pang & Bei Wu, 2024. "Estimation of Integrated Volatility Functionals with Kernel Spot Volatility Estimators," Papers 2407.09759, arXiv.org.
    • Handle: RePEc:arx:papers:2407.09759
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2407.09759
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    2. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Benth, Fred Espen & Schroers, Dennis & Veraart, Almut E.D., 2022. "A weak law of large numbers for realised covariation in a Hilbert space setting," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 241-268.
    2. YAMAMOTO, Yohei & 山本, 庸平, 2015. "Asymptotic Inference for Common Factor Models in the Presence of Jumps," Discussion Papers 2015-05, Graduate School of Economics, Hitotsubashi University.
    3. Ruijun Bu & Degui Li & Oliver Linton & Hanchao Wang, 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Working Papers 202212, University of Liverpool, Department of Economics.
    4. Aït-Sahalia, Yacine & Kalnina, Ilze & Xiu, Dacheng, 2020. "High-frequency factor models and regressions," Journal of Econometrics, Elsevier, vol. 216(1), pages 86-105.
    5. Dovonon, Prosper & Taamouti, Abderrahim & Williams, Julian, 2022. "Testing the eigenvalue structure of spot and integrated covariance," Journal of Econometrics, Elsevier, vol. 229(2), pages 363-395.
    6. Cheng, Mingmian & Swanson, Norman R. & Yang, Xiye, 2021. "Forecasting volatility using double shrinkage methods," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 46-61.
    7. Markus Bibinger, 2024. "Probabilistic models and statistics for electronic financial markets in the digital age," Papers 2406.07388, arXiv.org.
    8. Choi, Jungjun & Yang, Xiye, 2022. "Asymptotic properties of correlation-based principal component analysis," Journal of Econometrics, Elsevier, vol. 229(1), pages 1-18.
    9. 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.
    10. Richard Y. Chen, 2019. "The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations," Papers 1911.02205, arXiv.org.
    11. Chen, Dachuan, 2024. "High frequency principal component analysis based on correlation matrix that is robust to jumps, microstructure noise and asynchronous observation times," Journal of Econometrics, Elsevier, vol. 240(1).
    12. repec:hit:hiasdp:2015-04 is not listed on IDEAS
    13. Jos'e E. Figueroa-L'opez & Bei Wu, 2020. "Kernel Estimation of Spot Volatility with Microstructure Noise Using Pre-Averaging," Papers 2004.01865, arXiv.org, revised Feb 2022.
    14. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    15. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    16. Iara da Silva & Caroline Fernanda Hei Wikuats & Elizabeth Mie Hashimoto & Leila Droprinchinski Martins, 2022. "Effects of Environmental and Socioeconomic Inequalities on Health Outcomes: A Multi-Region Time-Series Study," IJERPH, MDPI, vol. 19(24), pages 1-22, December.
    17. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    18. Prosper Dovonon & Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2019. "Bootstrapping High-Frequency Jump Tests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 793-803, April.
    19. Reisenhofer, Rafael & Bayer, Xandro & Hautsch, Nikolaus, 2022. "HARNet: A convolutional neural network for realized volatility forecasting," CFS Working Paper Series 680, Center for Financial Studies (CFS).
    20. Tim Bollerslev & Jia Li & Yuan Xue, 2018. "Volume, Volatility, and Public News Announcements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2005-2041.
    21. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2019. "Is Volatility Rough ?," Papers 1905.04852, arXiv.org, revised May 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2407.09759. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.