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

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.