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We present a modified version of the non parametric Hawkes kernel estimationprocedure studied in arXiv:1401.0903 that is adapted to slowly decreasingkernels. We show on numerical simulations involving a reasonable number ofevents that this method allows us to estimate faithfully a power-law decreasingkernel over at least 6 decades. We then propose a 8-dimensional Hawkes modelfor all events associated with the first level of some asset order book.Applying our estimation procedure to this model, allows us to uncover the mainproperties of the coupled dynamics of trade, limit and cancel orders inrelationship with the mid-price variations.

Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling