A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data
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 <i>n</i> exchangeable and dependent units, which are becoming increasingly common in practice....
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/126 |
| _version_ | 1797442958602010624 |
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| author | Huaping Chen Jiayue Zhang Xiufang Liu |
| author_facet | Huaping Chen Jiayue Zhang Xiufang Liu |
| author_sort | Huaping Chen |
| collection | DOAJ |
| description | 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 <i>n</i> exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway–Maxwell–Poisson-binomial (CMPB) thinning operator and then establishes the Conway–Maxwell–Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model’s 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. |
| first_indexed | 2024-03-09T12:49:11Z |
| format | Article |
| id | doaj.art-96cc0eec29564892954ef1e70c0a62f7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T12:49:11Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-96cc0eec29564892954ef1e70c0a62f72023-11-30T22:09:02ZengMDPI AGEntropy1099-43002023-01-0125112610.3390/e25010126A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series DataHuaping Chen0Jiayue Zhang1Xiufang Liu2School of Mathematics and Statistics, Henan University, Kaifeng 475004, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaCollege of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaBinomial 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 <i>n</i> exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway–Maxwell–Poisson-binomial (CMPB) thinning operator and then establishes the Conway–Maxwell–Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model’s 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.https://www.mdpi.com/1099-4300/25/1/126CMPB thinning operatorbounded time seriesCMPBAR modelunder-dispersionequi-dispersionover-dispersion |
| spellingShingle | Huaping Chen Jiayue Zhang Xiufang Liu A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data Entropy CMPB thinning operator bounded time series CMPBAR model under-dispersion equi-dispersion over-dispersion |
| title | A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data |
| title_full | A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data |
| title_fullStr | A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data |
| title_full_unstemmed | A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data |
| title_short | A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data |
| title_sort | conway maxwell poisson binomial ar 1 model for bounded time series data |
| topic | CMPB thinning operator bounded time series CMPBAR model under-dispersion equi-dispersion over-dispersion |
| url | https://www.mdpi.com/1099-4300/25/1/126 |
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