Efficient estimation in (PINAR(1)) model: semiparametric case

Abstract

The efficient estimation problem of a semi-parametric first-order periodic integer-valued autoregressive (PINAR(1)) model is considered. The unspecified distribution of the innovation process of this model is suposed to satisfy only some mild technical assumptions. We therefore provide efficient estimates for both parameters of the model, namely a periodic autoregressive parameter and a periodic probability law of the innovation non-negative integer values process which is seen as an infinite dimensional parameter. The performances of these efficient estimations are shown through intensive simulations studies and an application on real data set.

Keywords:

• Periodically correlated integer-valued process
• (LAN) property
• Non-parametric maximum likelihood
• Periodic INAR(1) model
• Semiparametric efficient estimation

AMS SUBJECT CLASSIFICATION:

• 62 F12
• 62 M10

Acknowledgments

The authors would like to express their most sincere thanks and grateful to the anonymous referee for his precious suggestions, useful orientations, and many important remarks. They are also very grateful for his corrections and valuable suggestions which have further improved the first revised version.