Change Point Detection in Count Time Series: an empirical likelihood approach

Abstract

Change point detection is an important topic in time series analysis, aiming to identify the time points at which structural changes occur in the behavior of a stochastic process. This problem is particularly important and challenging for count time series due to the discrete nature of the data and the temporal dependence among observations. In this talk, structural changes in the parameters of count time series models are investigated using nonparametric approaches, with particular emphasis on empirical likelihood. Within this framework, empirical likelihood ratio statistics are constructed to test for the existence of a change point and to identify its location, without requiring the specification of a particular parametric distribution for the data. The main idea is to compare the model under parameter stability with an alternative in which the process parameters change at an unknown time point. The asymptotic properties of the proposed test statistics, including their limiting distributions under the null hypothesis and the consistency of the procedures for detecting structural changes, are discussed. The performance of the proposed methods is also evaluated through simulation studies under various scenarios, including different types and magnitudes of parameter changes and different sample sizes. Finally, applications to real count time series data are presented to illustrate the implementation of the proposed approaches in practical settings and their ability to identify structural changes in real-world data. The main objective of this talk is to provide a coherent framework for the use of empirical likelihood in change point detection for count time series and to discuss the theoretical and practical aspects of these approaches.