A note on an integer valued time series model with Poisson–negative binomial marginal distribution

Abstract

This paper proposes a new model for autoregressive time series of counts in terms of a convolution of Poisson and negative binomial random variables, known as Poisson–negative binomial (PNB) distribution. The corresponding first-order integer valued time series models are developed and their properties are discussed. The geometric PNB and the geometric semi PNB distributions are also introduced and studied.

Keywords:

• Count data models
• Discrete self-decomposability
• INAR models
• Infinite divisibility
• Poisson-negative binomial distribution

Mathematics Subject Classification:

• Primary 62M10
• Secondary 62M15

Acknowledgments

The authors acknowledge the Editor and referees for the valuable suggestions which helped in improving the presentation of the paper.

Funding

The authors are also grateful to the University Grants Commission of India, New Delhi and Mahatma Gandhi University, Kottayam, for supporting this research.