Efficient estimation in periodic INAR(1) model: parametric case

Abstract

This paper focuses on the efficient estimation problem of a first-order Periodic Integer-Valued Autoregressive ($\mathit{\text{PINAR}}(1)$) Model. The Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ) and the Local Asymptotic Linearity property satisfied by its central sequence are established. By using these results, we construct efficient estimators for the parameters in the parametric case. The consistency property of these efficient estimations are shown via intensive simulation studied. Moreover, the performance of these efficient estimations, over the Conditional Maximum Likelihood (CML), the Yule-Walker (YW) and the Conditional Least Squares (CLS) estimations, is also shown via intensive simulation studied and an application on real data set.

KEYWORDS:

• Periodically correlated integer-valued process
• Periodic $\mathit{\text{INAR}}(1)$ model
• Mean and second moment periodically stationary
• Efficient estimation

AMS SUBJECT CLASSIFICATION:

• 62F12
• 62M10

Acknowledgments

The authors express their most sincere thanks and grateful acknowledgements to the two anonymous referees for their valuable remarks, constructive suggestions and corrections that permitted us to improve the quality and the readability of the paper.