On some periodic INARMA(p,q) models

Abstract

This paper deals with the study of some probabilistic and statistical properties of some particular models of the class of Periodic Integer-Valued Autoregressive Moving Average, PINARMA(p, q), Models. For any considered particular model, the necessary and sufficient conditions for the periodically stationary in the first and second order, are established. The closed forms of the mean and the variance are obtained. The autocovariance structure is studied. The estimation of the parameters are obtained by the Yule-Walker (YW) method and the Conditional Least Squares (CLS) method. The performances of these estimators are assisted by a simulation illustration. Moreover, an application on real data set is provided.

KEYWORDS:

• Periodic integer-valued autoregressive moving average
• Periodically correlated process
• Periodically stationary condition

AMS subject classification:

• 62F12
• 62M10

Acknowledgments

The authors express their most sincere thanks and grateful acknowledgements to the associate editor’s and to the anonymous reviewers for their valuable comments and constructive suggestions that greatly improved the paper.

Notes

1 The authors present their deep acknowledgments to Dr. Xanthi Pedeli, Ca’ Foscari University of Venice (Italy) for contributing the accidents counts data.