Negative Binomial Autoregression: A Tractable Model with Composite Likelihood-Based Inference

In this work we propose a count autoregression model with negative binomial marginals for analyzing overdispersed count time series data. Properties of the proposed count model are established. Our approach is to develop a method for inference based on a composite likelihood function. The strong consistency and the asymptotic normality of the maximum composite likelihood estimators are established. We derive a procedure for calculating the standard error of the parameter estimates and confidence intervals based on a parametric bootstrap. We also present prediction based on our negative binomial autoregression and propose diagnostic tools based on a standardized Pearson residual in order to check model adequacy. Monte Carlo experiments were conducted to study and compare the finite-sample properties of the proposed estimators. The simulations demonstrate that, compared to the generalized linear model approach combined 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 misspecification. An empirical illustration about the number of cases of campylobacter infections in the north of the province Quebec (Canada) in four week intervals from January 1990 to the end of October 2000 is presented. Joint work with Hernando Ombao (KAUST - Arábia Saudita).