Mutually Exciting Point Processes with Latency

• 成果类型: Article; Early Access
• 署名作者: Potiron, Yoann; Volkov, Vladimir
• 署名单位: Keio University; University of Tasmania; HSE University (National Research University Higher School of Economics)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2516209
• 发表日期: 2025
• 关键词: hawkes processes; inference; MARKET; SPECTRA; RISK

摘要

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 United States and Canadian stock exchanges vary between 1 and 6 milliseconds from 2020 to 2021. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.