{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T07:07:40Z","timestamp":1774508860849,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T00:00:00Z","timestamp":1673049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Henan Province","award":["222300420127"],"award-info":[{"award-number":["222300420127"]}]},{"name":"Natural Science Foundation of Henan Province","award":["202103051"],"award-info":[{"award-number":["202103051"]}]},{"name":"Natural Science Foundation of Henan Province","award":["202103021223084"],"award-info":[{"award-number":["202103021223084"]}]},{"name":"Postdoctoral research in Henan Province","award":["222300420127"],"award-info":[{"award-number":["222300420127"]}]},{"name":"Postdoctoral research in Henan Province","award":["202103051"],"award-info":[{"award-number":["202103051"]}]},{"name":"Postdoctoral research in Henan Province","award":["202103021223084"],"award-info":[{"award-number":["202103021223084"]}]},{"name":"Basic Research Programs of Shanxi Province","award":["222300420127"],"award-info":[{"award-number":["222300420127"]}]},{"name":"Basic Research Programs of Shanxi Province","award":["202103051"],"award-info":[{"award-number":["202103051"]}]},{"name":"Basic Research Programs of Shanxi Province","award":["202103021223084"],"award-info":[{"award-number":["202103021223084"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Binomial autoregressive models are frequently used for modeling bounded time series counts. However, they are not well developed for more complex bounded time series counts of the occurrence of n exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway\u2013Maxwell\u2013Poisson-binomial (CMPB) thinning operator and then establishes the Conway\u2013Maxwell\u2013Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model\u2019s parameters, and establish the asymptotic normality of the CML estimator. In a simulation study, the boxplots illustrate that the CML estimator is consistent and the qqplots show the asymptotic normality of the CML estimator. In the real data example, our model takes a smaller AIC and BIC than its main competitors.<\/jats:p>","DOI":"10.3390\/e25010126","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T02:09:39Z","timestamp":1673230179000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Conway\u2013Maxwell\u2013Poisson-Binomial AR(1) Model for Bounded Time Series Data"],"prefix":"10.3390","volume":"25","author":[{"given":"Huaping","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Henan University, Kaifeng 475004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayue","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiufang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1214\/aop\/1176994950","article-title":"Discrete analogues of self-decomposability and stability","volume":"7","author":"Steutel","year":"1979","journal-title":"Ann. 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