First-order random coefficient mixed-thinning integer-valued autoregressive model

Abstract

The paper develops a first-order random coefficient mixed-thinning integer-valued autoregressive time series model (RCMTINAR(1)) to deal with the data related to the counting of elements of variable character. Moments and autocovariance functions for this model are studied as the distribution of the innovation sequence is unknown. The conditional least squares and modified quasi-likelihood are adopted to estimate the model parameters. Asymptotic properties of the obtained estimators are established. The performances of these estimators are investigated and compared with false modified quasi-likelihood via simulations. Finally, the practical relevance of the model is illustrated by using two applications to a SIMpass data set and a burglary data set with a comparison with relevant models that exist so far in the literature.