IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1112.1838.html
   My bibliography  Save this paper

Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data

Author

Listed:
  • E. Bacry
  • K. Dayri
  • J. F. Muzy

Abstract

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation function is computed using a minimal phase recovering method. We illustrate our method on some examples and provide an empirical study of the estimation errors. Within this framework, we analyze high frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowly decaying (power-law) kernel shapes suggesting a long memory nature of self-excitation phenomena at the microstructure level of price dynamics.

Suggested Citation

  • E. Bacry & K. Dayri & J. F. Muzy, 2011. "Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data," Papers 1112.1838, arXiv.org.
    • Handle: RePEc:arx:papers:1112.1838
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1112.1838
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
    2. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    3. Ioane Muni Toke, 2011. ""Market making" behaviour in an order book model and its impact on the bid-ask spread," Post-Print hal-01705266, HAL.
    4. Mohler, G. O. & Short, M. B. & Brantingham, P. J. & Schoenberg, F. P. & Tita, G. E., 2011. "Self-Exciting Point Process Modeling of Crime," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 100-108.
    5. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    2. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    3. Etienne Chevalier & Yadh Hafsi & Vathana Ly Vath, 2023. "Uncovering Market Disorder and Liquidity Trends Detection," Papers 2310.09273, arXiv.org.
    4. Ban Zheng & Franc{c}ois Roueff & Fr'ed'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.

    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. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    2. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
    3. Angelos Dassios & Hongbiao Zhao, 2017. "A Generalized Contagion Process With An Application To Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-33, February.
    4. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    5. Dassios, Angelos & Zhao, Hongbiao, 2017. "A generalised contagion process with an application to credit risk," LSE Research Online Documents on Economics 68558, London School of Economics and Political Science, LSE Library.
    6. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    7. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    8. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    9. Emmanuel Bacry & Jean-Francois Muzy, 2014. "Second order statistics characterization of Hawkes processes and non-parametric estimation," Papers 1401.0903, arXiv.org, revised Feb 2015.
    10. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org.
    11. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    12. Steffen Volkenand & Günther Filler & Martin Odening, 2020. "Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities," Risks, MDPI, vol. 8(3), pages 1-17, July.
    13. Cavaliere, Giuseppe & Lu, Ye & Rahbek, Anders & Stærk-Østergaard, Jacob, 2023. "Bootstrap inference for Hawkes and general point processes," Journal of Econometrics, Elsevier, vol. 235(1), pages 133-165.
    14. Ulrich Horst & Wei Xu, 2024. "Functional Limit Theorems for Hawkes Processes," Papers 2401.11495, arXiv.org.
    15. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    16. Clements, Adam & Liao, Yin, 2017. "Forecasting the variance of stock index returns using jumps and cojumps," International Journal of Forecasting, Elsevier, vol. 33(3), pages 729-742.
    17. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    18. Volodymyr Korniichuk, 2012. "Forecasting extreme electricity spot prices," Cologne Graduate School Working Paper Series 03-14, Cologne Graduate School in Management, Economics and Social Sciences.
    19. Giacomo Bormetti & Lucio Maria Calcagnile & Michele Treccani & Fulvio Corsi & Stefano Marmi & Fabrizio Lillo, 2015. "Modelling systemic price cojumps with Hawkes factor models," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1137-1156, July.
    20. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    21. Angelos Dassios & Jiwook Jang & Hongbiao Zhao, 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance," Risks, MDPI, vol. 7(4), pages 1-18, October.

    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:1112.1838. 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.