On shifted integer-valued autoregressive model for count time series showing equidispersion, underdispersion or overdispersion

In this paper, we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning. This model is suitable to modeling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2021-09, Vol.50 (20), p.4822-4843
Main Authors: da Cunha, Enai Taveira, Bourguignon, Marcelo, Vasconcellos, Klaus L. P.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic normality
Autoregressive models
Autoregressive processes
binomial thinning operator
borel distribution
Estimators
integer-valued time series model
Integers
Model testing
Monte Carlo simulation
Parameter estimation
Time series
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Summary:In this paper, we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning. This model is suitable to modeling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are obtained. To estimate the unknown parameters, the Yule-Walker (YW), conditional least squares (CLS) and conditional maximum likelihood (CML) methods are considered. The asymptotic distribution of CLS estimators are obtained and hypothesis tests to test an equidispersed model against an underdispersed or overdispersed model are formulated. A Monte Carlo simulation is presented analyzing the estimators performance in finite samples. Two applications to real data are presented to show that the Borel INAR(1) model is suited to model underdispersed and overdispersed data counts.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2020.1725822