We propose a log-linear Poisson regression model driven by a stationary latent gamma autoregression. This process has negative binomial (NB) marginals to analyze overdispersed count time series data. Estimation and statistical inference are performed using a composite (CL) likelihood function. We establish theoretical properties of the proposed count model, in particular, the strong consistency and asymptotic normality of the maximum CL estimator. A procedure for calculating the standard error of the parameter estimator and confidence intervals is derived based on the parametric bootstrap. Monte Carlo experiments were conducted to study and compare the finite-sample properties of the proposed estimators. The simulations demonstrate that, compared with the approach that combines generalized linear models with the ordinary least squares method, the proposed composite likelihood approach provides satisfactory results for estimating the parameters related to the correlation structure of the process, even under model misspecification. An empirical illustration of the NB process is presented for the monthly number of viral hepatitis cases in Goiânia (capital and largest city of the Brazilian state of Goiás) from January 2001 to December 2018.

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负二项式过程：具有基于复合似然推理的易处理模型

我们提出了一个由平稳潜在伽马自回归驱动的对数线性泊松回归模型。此过程具有负二项式 (NB) 边际以分析过度分散的计数时间序列数据。使用复合 (CL) 似然函数执行估计和统计推断。我们建立了所提出的计数模型的理论性质，特别是最大 CL 估计量的强一致性和渐近正态性。计算参数估计器的标准误差和置信区间的过程是基于参数引导程序得出的。进行了蒙特卡罗实验来研究和比较所提出的估计器的有限样本特性。仿真表明，与将广义线性模型与普通最小二乘法相结合的方法相比，所提出的复合似然方法为估计与过程的相关结构相关的参数提供了令人满意的结果，即使在模型错误指定的情况下也是如此。对 2001 年 1 月至 2018 年 12 月戈亚尼亚（巴西戈亚斯州首府和最大城市）每月病毒性肝炎病例数进行了 NB 过程的实证说明。