Statistical inference for first-order random coefficient integer-valued autoregressive processes

In this paper, we apply the least-squares method to estimate the unknown parameters in first-order random coefficient integer-valued autoregressive ( $\operatorname{RCINAR}(1)$ ) processes. The least-squares estimator is derived and its limiting properties are discussed. Furthermore, we also derive a statistic to test the randomness of coefficients. Numerical results from simulation studies suggest that the proposed method is good for practical use.