基于普通最小二乘法的Hawkes过程参数估计

中文摘要 AI 辅助

我们开发了一类强度函数为参数形式的自激Hawkes过程的参数估计框架，该估计过程基于普通最小二乘法。为应用最小二乘估计，我们将核函数限制为可表示为参数与某函数乘积之和的核类。我们首先建立所提估计量的中心极限定理，随后证明渐近方差估计量的一致性，最后引入Wald检验统计量并推导其渐近分布。我们将该方法应用于高频金融资产数据的交易时间，实证结果提供了三类异质交易者的证据，其中两类为高频交易者，一类为基本面交易者。

英文摘要

We develop a parametric estimation framework for self-exciting Hawkes processes whose intensity functions admit a parametric form. The estimation procedure is based on ordinary least squares. To apply the least squares estimation, we restrict to a kernel class that can be expressed as a sum of the product of a parameter and a function. We first establish the central limit theorem for the proposed estimator. We then show the consistency of the asymptotic variance estimator. Finally, we introduce a Wald test statistic and derive its asymptotic distribution. We apply the proposed methodology to trade times from high-frequency financial asset data. Our empirical results provide evidence for three heterogeneous trader types. In particular, we identify two trader types as high-frequency traders and one trader type as fundamental trader.

发表机构

• Faculty of Science and Technology, Keio University（庆应义塾大学理工学部）
• Riken-AIP（理化学研究所人工智能研究中心）
• Faculty of Business and Commerce, Keio University（庆应义塾大学商学部）

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