A trinomial difference autoregressive process for the bounded ℤ -valued time series

This article tackles the modeling challenge of bounded $\mathbb{Z}$-valued time series by proposing a novel trinomial difference autoregressive process. This process not only maintains the autocorrelation structure presenting in the classical binomial GARCH model, but also facilitates the analysis of bounded $\mathbb{Z}$-valued time series with negative or positive correlation. We verify the stationarity and ergodicity of the couple process (comprising both the observed process and its conditional mean process) while also presenting several stochastic properties. We further discuss the conditional maximum likelihood estimation and establish their asymptotic properties. The effectiveness of these estimators is assessed through simulation studies, followed by the application of the proposed models to two real datasets.