A first-order random coefficient mixed-thinning threshold integer-valued autoregressive model to analyze the COVID-19 data

This article develops a first-order random coefficient mixed-thinning threshold integer-valued autoregressive (RCMTTINAR(1)) model to deal with the data related to the segmented phenomena and variable character element features, where the distribution of the innovation sequence is unknown. Stationarity and ergodicity properties of the proposed model are derived. The conditional least squares estimation method and the modified quasi-likelihood estimation method are adopted to estimate the model parameters and the nested subsample search (NeSS) algorithm is used to estimate the threshold parameter r. The asymptotic properties of the obtained estimators are established, and the performances of the estimation methods are studied through simulation experiments. Finally, the practical relevance of the model is illustrated by using the COVID-19 data on suspected cases imported from abroad with a comparison with relevant models that exist in the literature.