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 to 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 \texttt{CptPointProcess}.

翻译：变点检测的目标在于识别时间序列数据中的行为转变。本文聚焦于数据来源于非齐次泊松过程或标记泊松过程的情形。我们提出了一种使用最小对比估计器检测多重离线变点的方法。具体而言，我们探讨了如何在给定离散观测值的情况下处理过程的连续性。此外，我们通过交叉验证程序选择了合适的变点数量，该程序特别适用于泊松过程的特性。最后，我们展示了如何将这种方法应用于强度发生变化的自我激励过程。通过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包 \texttt{CptPointProcess} 中实现。