An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data
Time series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other...
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| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231491?viewType=HTML |
| _version_ | 1797629015032332288 |
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| author | Kee Wah Fo Seng Huat Ong Choung Min Ng You Beng Koh |
| author_facet | Kee Wah Fo Seng Huat Ong Choung Min Ng You Beng Koh |
| author_sort | Kee Wah Fo |
| collection | DOAJ |
| description | Time series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other distributions such as the generalized Poisson, double Poisson, hyper-Poisson, and COM-Poisson distributions have been proposed to replace the Poisson distribution to model the different levels of dispersion in time series of counts. These models have certain limitations such as complex expressions for the mean and variance which complicate the formulation as GARCH models. In this study, we propose an alternative hyper-Poisson (AHP) distribution, with simple forms of conditional mean and variance, for an integer-valued GARCH (INGARCH) model for time series of counts that also exhibit the different levels of dispersion. We demonstrate that the AHP-INGARCH model is comparable to some existing INGARCH models. Additionally, the model can cover a wider range of dispersion. The maximum likelihood estimation can be used to estimate the parameters of the proposed model. Applications to three real-life data sets related to polio, internet protocol and daily COVID-19 new deaths underscore the usefulness of the proposed model in studying both over-dispersed and under-dispersed time series of counts. |
| first_indexed | 2024-03-11T10:47:25Z |
| format | Article |
| id | doaj.art-c4be27eaaf874bc3820154b6ef6fb926 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T10:47:25Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c4be27eaaf874bc3820154b6ef6fb9262023-11-14T01:11:34ZengAIMS PressAIMS Mathematics2473-69882023-10-01812291162913910.3934/math.20231491An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 dataKee Wah Fo0Seng Huat Ong1Choung Min Ng2You Beng Koh 31. Faculty of Engineering and Quantity Surveying, INTI International University, Persiaran Bandar Baru Nilai, 71800 Nilai, Malaysia2. Institute of Actuarial Science and Data Analytics, UCSI University, 56000 Kuala Lumpur, Malaysia 3. Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia3. Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia3. Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, MalaysiaTime series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other distributions such as the generalized Poisson, double Poisson, hyper-Poisson, and COM-Poisson distributions have been proposed to replace the Poisson distribution to model the different levels of dispersion in time series of counts. These models have certain limitations such as complex expressions for the mean and variance which complicate the formulation as GARCH models. In this study, we propose an alternative hyper-Poisson (AHP) distribution, with simple forms of conditional mean and variance, for an integer-valued GARCH (INGARCH) model for time series of counts that also exhibit the different levels of dispersion. We demonstrate that the AHP-INGARCH model is comparable to some existing INGARCH models. Additionally, the model can cover a wider range of dispersion. The maximum likelihood estimation can be used to estimate the parameters of the proposed model. Applications to three real-life data sets related to polio, internet protocol and daily COVID-19 new deaths underscore the usefulness of the proposed model in studying both over-dispersed and under-dispersed time series of counts.https://www.aimspress.com/article/doi/10.3934/math.20231491?viewType=HTMLalternative hyper-poissoninteger-valued garchtime series of countspoliointernet protocolcovid-19 |
| spellingShingle | Kee Wah Fo Seng Huat Ong Choung Min Ng You Beng Koh An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data AIMS Mathematics alternative hyper-poisson integer-valued garch time series of counts polio internet protocol covid-19 |
| title | An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data |
| title_full | An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data |
| title_fullStr | An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data |
| title_full_unstemmed | An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data |
| title_short | An alternative hyper-Poisson integer-valued GARCH model with application to polio, internet protocol and COVID-19 data |
| title_sort | alternative hyper poisson integer valued garch model with application to polio internet protocol and covid 19 data |
| topic | alternative hyper-poisson integer-valued garch time series of counts polio internet protocol covid-19 |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231491?viewType=HTML |
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