Poisson QMLE for change-point detection in general integer-valued time series models

TL;DR

This paper introduces Poisson QMLE-based procedures for detecting change-points in integer-valued time series, demonstrating their consistency and effectiveness through simulations and real data analysis.

Contribution

It develops new change-point detection methods using Poisson quasi-maximum likelihood estimators applicable to general integer-valued time series models.

Findings

Test statistics converge to Brownian motion distributions under null hypothesis.

Procedures are consistent, diverging under the alternative hypothesis.

Simulation and real data results validate the methods.

Abstract

We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We propose procedures which are based on the Poisson quasi-maximum likelihood estimator of the parameter, and where the updated estimator is computed without the historical observations in the sequential framework. For both the retrospective and the sequential detection, the test statistics converge to some distributions obtained from the standard Brownian motion under the null hypothesis of no change and diverge to infinity under the alternative; that is, these procedures are consistent. Some results of simulations as well as real data application are provided.