On higher-order moments of INGARCH processes

For important count distributions, such as (zero-inflated) Poisson and (negative-)binomial, the kth factorial moment is proportional to the kth power of the mean. This property is utilized to derive a general approach for computing higher-order moments of integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) processes. The proposed approach covers a wide range of existing model specifications, and its potential benefits are illustrated by an analysis of skewness and excess kurtosis in INGARCH processes.