Multiple change-point detection for some point processes

TL;DR

This paper introduces a new method for detecting multiple change-points in inhomogeneous Poisson and marked Poisson processes, utilizing a minimum contrast estimator and cross-validation, with implementation in an R package.

Contribution

It presents a novel approach for offline change-point detection in point processes, addressing continuous data and model selection, with validation on simulated and real datasets.

Findings

Effective detection of multiple change-points in Poisson processes

Improved model selection via cross-validation tailored for point processes

Successful application demonstrated with real and simulated data

Abstract

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}.