Bivariate random coefficient integer‐valued autoregressive models: Parameter estimation and change point test

This study examines a first‐order bivariate random coefficient integer‐valued autoregressive (BRCINAR) model and the inferential procedures of this model, such as the parameter estimation and parameter change test. We first introduce the BRCINAR model and investigate its probabilistic properties such as stationarity, ergodicity, and high moment conditions, and then propose estimation methods such as the conditional least squares (CLS), modified quasi‐likelihood (MQL), and exponential family quasi‐likelihood (EQL) methods. As an application, a parameter change test is considered. For this task, a residual‐based cumulative sum (CUSUM) test is employed. To evaluate the performances of the three estimation methods and the respective CUSUM tests, we conduct a Monte Carlo simulation study and demonstrate the adequacy of the proposed methods. A real data analysis is also carried out using syphilis data in the United States for illustration.