Poisson difference integer valued autoregressive model of order one

This paper aims to model integer valued time series with possible negative values and either positive or negative correlations by introducing the Poisson difference integer valued autoregressive model of order one. This model has Poisson difference marginal distribution and is defined by a new operator called the extended binomial thinning operator. It includes previous integer valued autoregressive of order one model as special cases. The model can be used as a tool to model non-stationary count data. The model is applied to data from the Saudi stock exchange.