The negative binomial process: A tractable model with composite likelihood‐based inference

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