Maximum likelihood estimation of the SDMINAR(p) model to analyze some COVID-19 data

Motivated by a certain type of infinite-patch metapopulation model, this current work proposes a new mixed INAR(p) model (SDMINAR(p)) based on binomial thinning and negative binomial thinning operators, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the population at time {t−1,t−2,…,t−p} are large. Strict stationarity ergodicity property is proved. Conditional maximum likelihood estimation are adopted to estimate the model parameters. Asymptotic normality property of the estimators are displayed. The performances of the estimators are investigated in simulation, which manifests that the maximum likelihood estimation performs better when sample size increases. Finally, the practical relevance of the model is demonstrated by the COVID-19 data of suspected cases and severe cases imported from outside China with a comparison with relevant models that exist so far in the literature.