This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an extension of the Hawkes process, facilitating intensity modeling. This model's nature enables a filtered historical simulation that more accurately incorporates the properties of the original time series. Furthermore, the process extends to multivariate models with manageable estimation and simulation implementations. We investigate the impact of a flexible residual distribution on the estimation of high-frequency financial data, comparing it with the Hawkes process.

翻译：本文提出了一种自激励与互激励点过程，该过程通过离散马尔可夫动力学嵌入灵活的残差与强度。通过允许整合多样的残差分布，该模型可作为霍克斯过程的扩展，从而促进强度建模。该模型的特性使其能够实现一种过滤历史模拟，该模拟能更准确地纳入原始时间序列的性质。此外，该过程可扩展至多元模型，并具有可管理的估计与模拟实现方案。我们研究了灵活残差分布对高频金融数据估计的影响，并将其与霍克斯过程进行了比较。