On Exponential‐Family INGARCH Models

ABSTRACT A range of integer‐valued generalised autoregressive conditional heteroscedastic (INGARCH) models have been proposed in the literature, including those based on conditional Poisson, negative binomial and Conway‐Maxwell‐Poisson distributions. This note considers a larger class of exponential‐family INGARCH models, showing that maximum empirical likelihood estimation over this semiparametric class of models can lead to consistent estimates as well as unbiased inferences on model parameters. The proposed framework is tested on two data analysis examples and a simulation study.