We introduce a new model which can be considered as a extended version of the Hawkes process in a discrete sense. This model enables the integration of various residual distributions while preserving the fundamental properties of the original Hawkes process. The rich nature of this model enables a filtered historical simulation which incorporate the properties of original time series more accurately. The process naturally extends to multi-variate models with easy implementations of estimation and simulation. We investigate the effect of flexible residual distribution on estimation of high frequency financial data compared with the Hawkes process.

翻译：我们提出一种新模型，该模型可视为霍克斯过程在离散意义下的推广版本。该模型在保留原始霍克斯过程基本性质的同时，能够整合多种残差分布。其丰富的特性使得滤波历史模拟能够更准确地融入原始时间序列的特征。该过程自然扩展至多变量模型，且易于实现估计与模拟。我们研究了与霍克斯过程相比，灵活残差分布对高频金融数据估计的影响。