In the current study, a brand-new SINARS(1) model is proposed for stationary discrete time series defined on $\boldsymbol{Z}$, based on extended binomial distribution and the Pegram's operator. The model effectively characterizes the series of positive and negative integer values generated after differencing some non-stationary time series. The model's attributes are addressed. For the parameter estimation of the model, the conditional maximum likelihood method and Yule-Walker method are taken into consideration. And we prove the asymptotic normality of CML method. By using these two methods, we simulate our model comparing with some relevant ones proposed before. The model can deal with positive or negative autocorrelation data. The analysis of the number of differenced daily new cases in Barbados is done using the suggested model.

翻译：本研究基于扩展二项分布与Pegram算子，针对定义在$\boldsymbol{Z}$上的平稳离散时间序列，提出了一种全新的SINARS(1)模型。该模型能有效刻画非平稳时间序列经差分后生成的正负整数值序列的特征。本文探讨了该模型的相关属性。在参数估计方面，分别考虑了条件极大似然法和Yule-Walker方法，并证明了条件极大似然估计的渐近正态性。通过这两种方法，我们将所提模型与先前提出的若干相关模型进行了模拟对比。该模型可处理正自相关或负自相关的数据。最后，将该模型应用于巴巴多斯每日新增病例差分数据的分析。