  The Tick library allows researchers in market microstructure to simulate and
learn Hawkes process in high-frequency data, with optimized parametric and
non-parametric learners. But one challenge is to take into account the correct
causality of order book events considering latency: the only way one order book
event can influence another is if the time difference between them (by the
central order book timestamps) is greater than the minimum amount of time for
an event to be (i) published in the order book, (ii) reach the trader
responsible for the second event, (iii) influence the decision (processing time
at the trader) and (iv) the 2nd event reach the order book and be processed.
For this we can use exponential kernels shifted to the right by the latency
amount. We derive the expression for the log-likelihood to be minimized for the
1-D and the multidimensional cases, and test this method with simulated data
and real data. On real data we find that, although not all decays are the same,
the latency itself will determine most of the decays. We also show how the
decays are related to the latency. Code is available on GitHub at
https://github.com/MarcosCarreira/Hawkes-With-Latency.

Machine Learning;Machine Learning;Trading and Market Microstructure