A Parametric Study for the First-Order Signed Integer-Valued Autoregressive Process

In recent years, many attempts have been made to find accurate models for integer-valued times series. The SINAR (for Signed INteger-valued AutoRegressive) process is one of the most interesting. Indeed, the SINAR model allows negative values both for the series and its autocorrelation function. In this paper, we focus on the simplest SINAR(1) model under some parametric assumptions. Explicitly, we give an implicit form of the stationary distribution for a known innovation. Simulation experiments and analysis of real data sets are carried out to attest to the model’s performance.