Inference for Multiple Change-Points in Generalized Integer-Valued Autoregressive Model

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 versus LRSM with the multiple window parameter $h_{\text {mix}}$ 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.

Keywords

Piecewise stationary GCINAR process / Multiple change-points estimation / Likelihood ratio / Confidence interval / Count time series / 62M10 / 62J20

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Funding

National Natural Science Foundation of China(12271231)

Rights & permissions

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature