Abstract

Compared with low frequency data, high frequency data exhibit distinct empirical properties, including, for instance, essentially discontinuous evolution paths, time-varying intensities, and self-exciting features. All these make it more challenging to model appropriately the dynamics associated with high frequency data such as order arrival and price formation. To capture more accurately the microscopic structures and properties pertaining to the limit order books, this paper focuses on modeling high frequency data using Hawkes processes. Two models, one with exponential kernels and the other with power-law kernels, are introduced systematically, algorithmized precisely, and compared with each other extensively from various perspectives, including the goodness of fit to the original data and the computational time in searching for the maximum likelihood estimator, with search algorithm being taken into consideration as well. To measure the goodness of fit, a number of quantities are proposed. Studies based on both multiple-trading-day data of one stock and multiple-stock data on one trading day indicate that Hawkes processes with slowly-decaying kernels are able to reproduce the intensity of jumps in the price processes more accurately. The results suggest that Hawkes processes with power-law kernels and their implied long memory nature of self-excitation phenomena could, on the level of microstructure, serve as a realistic model for high frequency data.

摘要

与低频数据相比，高频数据表现出明显的经验特性，包括，例如，本质上不连续的演化路径、时变强度和自激特征。所有这些使得对与高频数据（例如订单到达和价格形成）相关的动态进行适当建模变得更具挑战性。为了更准确地捕捉与限价订单簿相关的微观结构和属性，本文侧重于使用霍克斯过程对高频数据进行建模。系统地介绍了指数核和幂律核两种模型，对其进行了精确的算法化处理，并从不同的角度进行了广泛的比较，包括原始数据的拟合优度和搜索最大似然估计的计算时间，同时还考虑了搜索算法。为了衡量拟合优度，提出了一些量。基于一只股票的多个交易日数据和一个交易日的多只股票数据的研究表明，具有缓慢衰减内核的霍克斯过程能够更准确地再现价格过程中的跳跃强度。结果表明，具有幂律核的霍克斯过程及其隐含的自激现象的长记忆性质，在微观结构层面上，可以作为高频数据的现实模型。提出了一些数量。基于一只股票的多个交易日数据和一个交易日的多只股票数据的研究表明，具有缓慢衰减内核的霍克斯过程能够更准确地再现价格过程中的跳跃强度。结果表明，具有幂律核的霍克斯过程及其隐含的自激现象的长记忆性质，在微观结构层面上，可以作为高频数据的现实模型。提出了一些数量。基于一只股票的多个交易日数据和一个交易日的多只股票数据的研究表明，具有缓慢衰减内核的霍克斯过程能够更准确地再现价格过程中的跳跃强度。结果表明，具有幂律核的霍克斯过程及其隐含的自激现象的长记忆性质，在微观结构层面上，可以作为高频数据的现实模型。