Epidemic change-point detection in general integer-valued time series

TL;DR

This paper develops a method for detecting epidemic change-points in discrete-valued time series, using a Poisson QMLE approach, with proven consistency and demonstrated effectiveness on simulated and real data.

Contribution

It introduces a new epidemic change-point detection test for integer-valued time series based on Poisson QMLE, with theoretical guarantees and practical validation.

Findings

Test statistic converges to a Brownian bridge distribution under null hypothesis.

Test statistic diverges under epidemic change, ensuring detection power.

Method validated with simulated and real data examples.

Abstract

In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We provide sufficient conditions for the consistency and the asymptotic normality of the Poisson quasi-maximum likelihood estimator (QMLE) of the model. We consider an epidemic change-point detection and propose a test statistic based on the QMLE of the parameter. Under the null hypothesis of a constant parameter (no change), the test statistic converges to a distribution obtained from a difference of two Brownian bridge. The test statistic diverges to infinity under the epidemic alternative, which establishes that the proposed procedure is consistent in power. The effectiveness of the proposed procedure is illustrated by simulated and real data examples.