Epidemiological count time series often display challenging characteristics such as overdispersion, zero-inflation, and serial dependence. This study explores appropriate statistical frameworks for modelling such data, using daily COVID-19 mortality counts from South Africa and its three most populous provinces as a case study. The observed data exhibited strong serial autocorrelation, excess zeros, overdispersion, and time-varying volatility. To capture these dynamics, we employed hybrid models combining zero-inflated Poisson autoregressive (ZIPA) and zero-inflated negative binomial autoregressive (ZINBA) structures with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) component. Model comparisons using the Vuong test indicated that the ZINBA model offered a superior fit. Further, a GARCH model applied to the ZINBA residuals effectively accounted for residual heteroscedasticity, as validated by sign-bias testing. These results underscore the utility of integrating zero-inflated count mode.
Chavalala et al. (Sun,) studied this question.