Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data
CMAP UMR 7641 CNRS, École Polytechnique,
2 SPE UMR 6134 CNRS, Université de Corse, 20250 Corte, France
a e-mail: firstname.lastname@example.org
Received in final form: 5 March 2012
Published online: 22 May 2012
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.
Key words: Statistical and Nonlinear Physics
The financial data used in this paper have been provided by the company QuantHouse EUROPE/ASIA, http://www.quanthouse.com.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012