Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data
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.
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- Luc Bauwens & Nikolaus Hautsch, 2007.
"Modelling Financial High Frequency Data Using Point Processes,"
SFB 649 Discussion Papers
SFB649DP2007-066, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- BAUWENS, Luc & HAUTSCH, Nikolaus, 2006. "Modelling financial high frequency data using point processes," CORE Discussion Papers 2006080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & HAUTSCH, Nikolaus, . "Modelling financial high frequency data using point processes," CORE Discussion Papers RP 2123, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
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