Abstract
The count data model studied in the paper extends the Poisson model by allowing for overdispersion that is correlated over time. Alternative approaches to estimate nuisance parameters, required for the correction of the Poisson maximum likelihood covariance matrix estimator and for a quasi-likelihood estimator, are studied. The comparisons are mainly based on finite sample Monte Carlo experimentation. It is found that the Poisson maximum likelihood estimator with corrected covariance matrix estimators provide reliable inferences for longer time series. Overdispersion test statistics are wellbehaved, while conventional portmanteau statistics for white noise have too large sizes. Two empirical illustration are included. (A)