论文标题
带有Carma（P，Q）强度的Hawkes模型
A Hawkes model with CARMA(p,q) intensity
论文作者
论文摘要
在本文中，我们介绍了一个名为Carma（P，Q）的新模型作为具有指数内核的Hawkes模型，这意味着自相关函数的行为严格降低，并且从经验上证明了对自相关功能的单调性假设。提出的模型是一个霍克斯过程，其中强度遵循连续的时间自回归移动平均值（CARMA）过程，并特别能够重现更现实的依赖性结构。我们还研究了增量的强度和强混合特性的平稳性和阳性条件。此外，我们计算了可能性，提出了一种模拟方法，并讨论了基于自相关函数的估计方法。模拟和估计练习突出了Carma（P，Q）-Hawkes的主要特征。
In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity assumption on the autocorrelation function. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process and specifically is able to reproduce more realistic dependence structures. We also study the conditions of stationarity and positivity for the intensity and the strong mixing property for the increments. Furthermore we compute the likelihood, present a simulation method and discuss an estimation method based on the autocorrelation function. A simulation and estimation exercise highlights the main features of the CARMA(p,q)-Hawkes.
