Comparison of Inferential Methods for a Novel CMP Model

In many real-life instances, time series of counts are often exposed to the dispersion phenomenon while at the same time being influenced by some explanatory variables. This paper takes into account these two issues by assuming that the series of counts follow an observation-driven first-order integer-valued moving-average structure (INMA(1)) where the innovation terms are COM-Poisson (CMP) distributed under a link function characterized by time-independent covariates. The second part of the paper constitutes estimating the regression effects, dispersion and the serial parameters using popular estimation methods, mainly the Conditional Least Squares (CLS), Generalized Method of Moments and Generalized Quasi-Likelihood (GQL) approaches. The performance of these estimation methods is compared via simulation experiments under different levels of dispersion. Additionally, the suggested model is used to examine time series accident data from actual incidents in several Mauritius locations.