Abstract: By using k-order Poisson dependent-driven random coefficient mixed thinning integer-valued autoregressive model, we analyzed data with the counting of elements of variable character, gave  statistical properties of the model and conditional maximum likelihood estimation of parameters, and proved the asymptotic normality of the estimators. The numerical simulation results show that as the sample size increases, the parameter estimation gradually converges to the true value. The actual data analysis results  show  that the effectiveness of the proposed model.

Key words: k-order autoregressive model, Po-DDRCMTINAR(k) model, mixed thinning operator, conditional maximum likelihood estimation