A class of k th‐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 th‐order dependence‐driven random coefficient mixed thinning integer‐valued autoregressive time series model (DDRCMTINAR()) 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‐ 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.