A class of kth-order dependence-driven random coefficient mixed thinning integer-valued autoregressive process to analyse epileptic seizure data and COVID-19 data

Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of $k$th-order dependence-driven random coefficient mixed thinning integer-valued autoregressive time series model (DDRCMTINAR($k$)) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi-likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi-likelihood estimators perform better than the conditional least squares considering the proportion of within-$\Omega$ estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID-19 data of suspected cases in China.