On periodic integer-valued moving average (INMA (q)) models

Abstract

This paper deals with the study of some probabilistic and statistical properties of a Periodic Integer-Valued Moving Average Model ($PINM{A}_S(q)$) with Generalized Poisson and Negative Binomial innovation process, for modelling different types of dispersion in count time series. Some probabilistic properties of the process are obtained. Furthermore, the time reversibility of the model is discussed in detail. The estimation of the underlying parameters is obtained by the Conditional Least Squares method (CLS). A simulation study is carried out to evaluate the performance of the estimation method. Finally, an application on real data set is provided to show the ability of the model for fitting data.

Keywords:

• Periodic integer-valued moving average
• periodically correlated process
• time reversibility

AMS Subject Classifications:

• 62F12
• 62M10

Acknowledgments

The authors present their deep acknowledgments to Pr. Jonas Nordström, University of Copenhagen, for contributing the German guest nights counts data.

Disclosure statement

No potential conflict of interest was reported by the author(s).