Zero-and-one inflated Poisson–Lindley INAR(1) process for modelling count time series with extra zeros and ones. Issue 10 (3rd July 2022)

• Record Type: Journal Article
• Authors: Mohammadi, Z.; Sajjadnia, Z.; Bakouch, H. S.; Sharafi, M.
• Is Part Of: Journal of statistical computation and simulation. Volume 92:Issue 10(2022)
• Page Start: 2018
• Page End: 2040
• Publication Date: 2022-07-03
• Subjects: INAR process -- zero-and-one inflated negative binomial distribution -- Probability generating function -- zero-and-one inflated Poisson–Lindley distribution -- runs -- expected length of zeros and ones; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2021.2019255
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : In this paper, a first-order integer-valued autoregressive (INAR(1)) model with zero-and-one inflated Poisson–Lindley distributed innovations is presented. It is shown that the model represents a mixture of zero-and-one inflated geometric INAR(1) process and zero-and-one inflated negative binomial INAR(1) process. Moreover, some basic and conditional properties of this model are obtained. The distribution of the runs (the lengths of zeros and ones) is investigated. Some estimation methods are used to estimate the unknown parameters of the model and the asymptotic properties of the estimators are obtained. Using the conditional maximum likelihood estimation method, the model is fitted to a set of practical data, and the model is validated by some goodness-of-fit criteria.