On mixture periodic Integer-Valued ARCH models

Abstract

This paper deals with the study of Mixture Periodic Integer-Valued Autoregressive Conditionally Heteroskedastic models. Some theoretical properties of the model, such as the first and the second moment periodically stationary conditions, are established. Moreover, closed-forms of these moments are, under these conditions, derived. The estimation is done by the maximum likelihood via the iterative EM algorithm and the performance of this method is shown via an intensive simulation study. A comparative real data study is performed on a Campylobacteriosis time series.

Keywords:

• Periodically correlated integer-valued process
• Mixture Periodic Integer-Valued (MPINARCH)
• periodically stationary condition
• EM algorithm
• Campylobacteriosis

AMS subject classification:

• 62F12
• 62M10

Acknowledgments

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