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

Abstract

This paper deals with some probabilistic and statistical properties of a periodic generalized integer-valued autoregressive $\mathit{PINAR}(1)$ 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.

Keywords:

• Asymptotic distribution of $\mathit{CLS}$ estimators
• Periodically correlated integer-valued process
• Periodic INAR model

AMS SUBJECT CLASSIFICATION:

• 62F12
• 62M10

Acknowledgments

The authors would like to extend their sincere thanks and appreciation to the anonymous referees for their pleasant assistance, helpful suggestions, constructive comments, and many important corrections that allowed us to improve the quality and readability of the research.