Mutually exciting point processes with latency

Journal of the American Statistical Association. 2025. P. 1–28.

Volkov V., Potiron Y.

A novel statistical approach to estimating latency, defined as the time it takes to learn about anevent and generate response to this event, is proposed. Our approach only requires amultidimensional point process describing event times, which circumvents the use of moredetailed datasets which may not even be available. We consider the class of parametric Hawkesmodels capturing clustering effects and define latency as a known function of kernel parameters,typically the mode of kernel function. Since latency is not well-defined when the kernel isexponential, we consider maximum likelihood estimation in the mixture of generalized gammakernels case and derive the feasible central limit theory with in-fill asymptotics. As a byproduct,central limit theory for a latency estimator and related tests are provided. Our numerical studycorroborates the theory. An empirical application on high frequency data transactions from theNew York Stock Exchange and Toronto Stock Exchange shows that latency estimates for the USand Canadian stock exchanges vary between 1 and 6 milliseconds from 2020 to 2021.

Keywords: latency, Hawkes processes

Publication based on the results of: Economic and mathematical analysis of markets, games, and decision-making (2025)