Modeling and monitoring of a new random coefficients ℤ-valued autoregressive time series process

Integer-valued time series models have been widely used for analyzing count data in epidemiology, public safety, and finance. However, many real count processes exhibit non-stationary behavior and external covariate effects. Taking differences often yields a stationary but Z-valued series. To describe such dynamics, this paper proposes a new class of covariate-driven random coefficient Z-valued autoregressive models. The proposed model is constructed based on the signed binomial thinning operator and adopts the skew discrete Laplace distribution as the innovation distribution, allowing flexible modeling of heavy-tailed fluctuations. A smooth transition mechanism driven by external covariates is introduced into the random coefficient structure, so that the dependence parameter can evolve gradually between different regimes. Some basic probabilistic properties of the proposed model are established, and conditional maximum likelihood estimation is used for parameter estimation. As such processes are often subject to unobserved structural changes in practice, failure to detect them may lead to misleading inference and poor decision-making. To further monitor structural changes in the underlying dynamics, three two-sided control charts are developed to detect upward and downward mean shifts. Monte Carlo simulations show good finite-sample and monitoring performance, and a real data example is presented to demonstrate practical effectiveness.