A trinomial difference autoregressive process for the bounded Z‐valued time series
针对有界整数值时间序列的建模难题，提出一种新的三项差分自回归过程，能处理正负相关，并验证了平稳性与遍历性，通过模拟和实际数据验证了有效性。
This article tackles the modeling challenge of bounded ‐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 ‐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.