A skew integer-valued time-series process with generalized Poisson difference marginal distribution

ABSTRACT

In this article, we propose a new integer-valued autoregressive process with generalized Poisson difference marginal distributions based on difference of two quasi-binomial thinning operators. This model is suitable for data sets on = {…, −2, −1, 0, 1, 2, …} and can be viewed as a generalization of the Poisson difference INAR(1) process. An advantage of the difference of two generalized Poisson random variables is it can have longer or shorter tails compared to the Poisson difference distribution. We present some basic properties of the process like mean, variance, skewness, and kurtosis, and conditional properties of the process are derived. Yule–Walker estimators are considered for the unknown parameters of the model and a Monte Carlo simulation is presented to study the performance of estimators. An application to a real data set is discussed to show the potential for practice of our model.

KEYWORDS:

• Generalized Poisson process
• quasi-binomial distribution
• integer-valued time series

AMS SUBJECT CLASSIFICATION:

• 62M10

Acknowledgments

We thank the four anonymous referees and an associate editor for the constructive suggestions and comments.