Abstract: We used a p-order random coefficient integer autoregressive RCINAR(p) model with dependent Bernoulli counting series to solve the analysis problem  of data with correlated characteristics of counting variables. We obtained the statistical properties of the model, the conditional maximum likelihood estimation of the parameters, and their asymptotic normality, and the effectiveness of the model was verified through the analysis of actual data,  accurately capturing data  correlations and trends. These results show  that the estimators of the model converge to the true values as the sample size increases.

Key words: dependent Bernoulli counting series, random coefficient, conditional maximum likelihood estimation, asymptotic normality