Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics |
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Authors: | Emmanuel Bacry Thibault Jaisson Jean–François Muzy |
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Affiliation: | 1. CMAP, UMR CNRS 7641, Ecole Polytechnique, 91128 Palaiseau, France.;2. SPE, UMR CNRS 6134, Université de Corse, 20250 Corté, France. |
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Abstract: | We present a modified version of the non parametric Hawkes kernel estimation procedure studied in Bacry and Muzy [arXiv:1401.0903, 2014] that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that this method allows us to estimate faithfully a power-law decreasing kernel over at least six decades. We then propose a eight-dimensional Hawkes model for all events associated with the first level of some asset order book. Applying our estimation procedure to this model, allows us to uncover the main properties of the coupled dynamics of trade, limit and cancel orders in relationship with the mid-price variations. |
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Keywords: | Hawkes processes Kernel estimations Power law kernels High-frequency Order book dynamics Trades Limit orders Cancel orders Market impact |
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