An empirical comparison of parametric and semiparametric time series regression models for overdispersed count data

Count time series regression is of interest in diverse applications. Count data may be marginally, as well as conditionally overdispersed, in addition to being serially dependent. We propose a fully parametric approach and a semiparametric approach (in the Godambe-information sense), and compare model performance in simulation studies. Estimators from both approaches exhibit large relative bias, but their variability was similar. Our empirical study shows that while our semiparametric approach method is promising as a robust alternative to fully parametric count time series regression modelling, bias correction is needed.