A new INAR model based on Poisson-BE2 innovations

Abstract

In this paper, two-parameter Poisson binomial-exponential 2 (PBE2) distribution is firstly reviewed, then a new integer-valued autoregressive (INAR) model with PBE2 innovations is proposed. The definition and statistical properties of the proposed model are given, including the mean, variance, covariance, strict stationarity and ergodicity. Two-step conditional least squares and conditional maximum likelihood estimation methods are considered to estimate the parameters. To assess the proposed model, a crime data set is analyzed and a comparison with other competing INAR models is given, which shows that the proposed model yields a better performance.

Keywords:

• Estimation
• overdispersion
• Poisson-BE2 distribution
• time series of counts

Acknowledgements

We thank the anonymous referee for his/her insightful and constructive comments that greatly improve the overall presentation.

Additional information

Funding

Zhu’s work is supported by National Natural Science Foundation of China (Nos. 11871027, 11731015) and Natural Science Foundation of Jilin Province (No. 20210101143JC).