Inference for multiple change-points in generalized integer-valued autoregressive model

TL;DR

This paper introduces the likelihood ratio scan method (LRSM) for detecting multiple change-points in generalized integer-valued autoregressive models, offering computational efficiency and reliable confidence interval construction.

Contribution

The paper proposes a new LRSM approach with theoretical justification and efficient computation for multiple change-point detection in integer-valued autoregressive processes.

Findings

LRSM performs well in long and short time series with different change-point densities.

Bootstrap procedures provide accurate confidence intervals for change-points.

Simulation and real data confirm the method's effectiveness and consistency.

Abstract

In this paper, we propose a computationally valid and theoretically justified methods, the likelihood ratio scan method (LRSM), for estimating multiple change-points in a piecewise stationary generalized conditional integer-valued autoregressive process. LRSM with the usual window parameter $h$ is more satisfied to be used in long-time series with few and even change-points vs. LRSM with the multiple window parameter $h_{mix}$ performs well in short-time series with large and dense change-points. The computational complexity of LRSM can be efficiently performed with order $O((\log n)^3 n)$. Moreover, two bootstrap procedures, namely parametric and block bootstrap, are developed for constructing confidence intervals (CIs) for each of the change-points. Simulation experiments and real data analysis show that the LRSM and bootstrap procedures have excellent performance and are consistent with the theoretical analysis.