A time series model with Bernoulli counting series dependent high-order random coefficient INAR

This paper proposes a time series model with Bernoulli counting series dependent high-order random coefficient INAR and investigates its stationarity and ergodicity. The unknown parameters are estimated by the conditional least squares method and the modified quasi-likelihood estimator, with the asymptotic properties of these estimators rigorously established. Simulation studies are conducted to evaluate the performance of the proposed estimation approach, demonstrating that the modified quasi-likelihood estimator outperforms the conditional least squares estimator in certain regions of the parameter space. Furthermore, the practical utility of the model is illustrated through an empirical analysis of criminal intent crime data.