A first-order integer-valued autoregressive process with zero-modified Poisson-Lindley distributed innovations. Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Sharafi, M.; Sajjadnia, Z.; Zamani, A.
• Is Part Of: Communications in statistics. Volume 52:Issue 3(2023)
• Page Start: 685
• Page End: 702
• Publication Date: 2023-03-04
• Subjects: Binomial thinning operator -- INAR(1) process -- Poisson Lindley distribution -- Zero-modified Poisson-Lindley distribution; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2020.1864644
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: In this paper, we introduce a first-order integer-valued autoregressive process with zero-modified Poisson-Lindley distributed innovations based on the binomial thinning operator. Some statistical and conditional properties of the model are presented, several estimation methods are applied to estimate the unknown parameters and, for the Yule-Walker and conditional least square estimators, the asymptotic distributions are obtained. Besides, a simulation study is conducted to compare the performance of the proposed estimators and, finally, two real count time series data are applied to demonstrate the usefulness of the proposed model.