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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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    File URL: http://arxiv.org/pdf/1112.1838
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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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