Bivariate random coefficient integer‐valued autoregressive models: Parameter estimation and change point test
研究了一阶双变量随机系数整数值自回归模型，提出了条件最小二乘、修正拟似然和指数族拟似然三种估计方法，并基于残差累积和检验进行参数变点检验，通过模拟和美国梅毒数据验证了方法的有效性。
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.