State estimation for temporal point processes

TL;DR

This paper develops new methods for estimating the parameters of temporal point processes observed in incomplete data intervals, adapting spatial process tools for improved inference.

Contribution

It introduces a novel approach for inference on broken interval observations of point processes, deriving new distributions and estimation techniques.

Findings

Derived marginal and conditional distributions for various models

Demonstrated effectiveness through simulation studies

Analyzed real data set with proposed methods

Abstract

This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point processes. For a range of models, the marginal and conditional distributions are derived. We discuss likelihood based inference as well as parameter estimation using the method of moments, conduct a simulation study for the important special case of renewal processes and analyse a data set collected by Diggle and Hawtin.