The aim of change-point detection is to identify behavioral shifts within time series data. This article focuses on scenarios where the data is derived from an inhomogeneous Poisson process or a marked Poisson process. We present a methodology for detecting multiple offline change-points using a minimum contrast estimator. Specifically, we address how to manage the continuous nature of the process given the available discrete observations. Additionally, we select the appropriate number of changes via a cross-validation procedure which is particularly effective given the characteristics of the Poisson process. Lastly, we show how to use this methodology for self-exciting processes with changes in the intensity. Through experiments, with both simulated and real datasets, we showcase the advantages of the proposed method, which has been implemented in the R package.

翻译：变点检测的目的是识别时间序列数据中的行为变化。本文聚焦于数据源自非齐次泊松过程或标记泊松过程的场景。我们提出一种基于最小对比估计量的离线多重变点检测方法。具体而言，我们探讨如何在仅获取离散观测值的情况下处理过程的连续性质。此外，我们通过交叉验证方法选择适当的变点数量，该方法在泊松过程的特性下尤为有效。最后，我们展示了如何将该方法应用于强度发生变化的自激励过程。通过基于模拟和真实数据集的实验，我们展示了所提方法的优势，该方法已在R语言包中实现。