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

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  • 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
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    References listed on IDEAS

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    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. BAUWENS, Luc & HAUTSCH, Nikolaus, 2006. "Modelling financial high frequency data using point processes," LIDAM Discussion Papers CORE 2006080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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.
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    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.

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