Inference for a New Signed Integer Valued Autoregressive Model Based on Pegram's Operator

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.