On a periodic negative binomial SETINAR model

Abstract

In this paper, we introduce a class of periodic negative binomial self-exciting threshold integer-valued autoregressive model. The basic probabilistic and statistical properties of this class are studied. Furthermore, the existence of a high moment and the strict periodic stationarity as well as the ergodicity, are established. The periodic autocovariance structure is also considered. The Conditional Least Squares (CLS) and the Conditional Maximum Likelihood (CML) methods are applied to estimate the underlying parameters, while using the periodic adaptation of the Nested Sub-Sample Search (NeSS) algorithm, to estimate the periodic threshold parameter. The asymptotic properties of the estimators are obtained. The performance of the CLS and the CML are compared through an intensive simulation study. An application on a real data set is provided.

Keywords:

• Periodically correlated integer-valued process
• Periodic NBSETINAR model
• Strictly periodically stationary model

AMS SUBJECT CLASSIFICATION:

• 62F12
• 62M10

Acknowledgments

The authors would like to present to the two anonymous referees their most sincere thanks and their profound acknowledgments for their pleasant assistance, helpful suggestions, constructive comments, and many important corrections that have allowed us to improve the quality and the readability of the paper.