Value-correlation controlled integer-valued autoregressive process in random environment

The manuscript presents a new integer-valued first-order autoregressive process in a random environment, which is governed by two control processes. The first process defines the marginal distribu-tion, while the second regulates the correlation structure within the model. The properties of the proposed model are examined in detail, providing insights into its theoretical foundations and practical implications. Two methods for estimating the unknown parameters are introduced: the Yule-Walker estimator and the conditional maximum likelihood estimator. A series of simulations assesses the efficiency of these esti-mation techniques and demonstrates their performance across various scenarios. The effectiveness of the introduced model is further evaluated through its application to real-life data.