Asymptotic distribution of CLS estimators in the nearly unstable and unstable PINAR(1) model

This paper deals with some probabilistic and statistical properties of a periodic generalized integer-valued autoregressive PINAR(1) model. The autocovariance structure is studied while establishing the closed-form of the periodic autocorrelation function. The Conditional Least Squares CLS-estimators of the underlying parameters are obtained. In addition, the asymptotic distribution of these estimators is provided, whether the innovation process mean is considered to be known or not, also for the nearly unstable and unstable integer-valued autoregressive PINAR(1) model. The performance of these estimators and their asymptotic distribution behavior are shown via a simulation study.