Mutually Exciting Point Processes with Latency
提出一种仅需事件时间数据即可估计延迟（从事件发生到做出反应的时间）的统计方法，适用于高频交易等场景，并在纽交所和多伦多交易所数据中验证了延迟在1-6毫秒之间。
A novel statistical approach to estimating latency, defined as the time it takes to learn about an event and generate response to this event, is proposed. Our approach only requires a multidimensional point process describing event times, which circumvents the use of more detailed datasets which may not even be available. We consider the class of parametric Hawkes models 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 is exponential, we consider maximum likelihood estimation in the mixture of generalized gamma kernels 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 study corroborates the theory. An empirical application on high frequency data transactions from the New York Stock Exchange and Toronto Stock Exchange shows that latency estimates for the US and Canadian stock exchanges vary between 1 and 6 milliseconds from 2020 to 2021.