Journal of Mathematics and Statistics

Poisson Quasi-Maximum Likelihood Estimator-based CUSUM Test for Integer-Valued Time Series

Sangyeol Lee

Journal of Mathematics and Statistics


This study considers the parameter change test for integer-valued time series models based on the Poisson quasi-maximum likelihood estimates. As a change point test, we consider the score vector-based CUSUM test and show that its limiting null distribution takes the form of a function of Brownian bridges. Moreover, the residual-based CUSUM tests are considered as alternatives. For evaluation, we conduct a Monte Carlo simulation study with Poisson, zero-inflated Poisson, negative binomial and Conway-Maxwell integer-valued generalized autoregressive conditional heteroscedastic models andPoisson integer-valued autoregressive models, and compare the performance of the proposed CUSUM tests. Our findings confirm that the proposed test is a functional tool for detecting a change point when the underlying distribution is unspecified.


© 2019 Sangyeol Lee. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.