Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables
A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their...
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| Format: | Article |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1910 |
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| author | Nurulkamal Masseran Saiful Izzuan Hussain |
| author_facet | Nurulkamal Masseran Saiful Izzuan Hussain |
| author_sort | Nurulkamal Masseran |
| collection | DOAJ |
| description | A correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal distribution, heavy tails, and dynamic changes over time. Hence, they cannot generate highly accurate information. To overcome this issue, this study proposes a combination of the Generalized Autoregressive Conditional Heteroskedasticity model, Generalized Pareto distribution, and stochastic copulas as a tool to investigate the dependence structure between the PM<sub>10</sub> variable and other pollutant variables, including CO, NO<sub>2</sub>, O<sub>3</sub>, and SO<sub>2</sub>. Results indicate that the dynamic dependence structure between PM<sub>10</sub> and other pollutant variables can be described with a ranking of PM<sub>10</sub>–CO > PM<sub>10</sub>–SO<sub>2</sub> > PM<sub>10</sub>–NO<sub>2</sub> > PM<sub>10</sub>–O<sub>3</sub> for the overall time paths (<i>δ</i>) and the upper tail (<i>τ<sup>U</sup></i>) or lower tail (<i>τ<sup>L</sup></i>) dependency measures. This study reveals an evident correlation among pollutant variables that changes over time; such correlation reflects dynamic dependency. |
| first_indexed | 2024-03-10T15:10:17Z |
| format | Article |
| id | doaj.art-4068c6a9d7514c5789577d5b52425cbd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:10:17Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4068c6a9d7514c5789577d5b52425cbd2023-11-20T19:24:04ZengMDPI AGMathematics2227-73902020-10-01811191010.3390/math8111910Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant VariablesNurulkamal Masseran0Saiful Izzuan Hussain1Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor 43600, MalaysiaA correlation analysis of pollutant variables provides comprehensive information on dependency behaviour and is thus useful in relating the risk and consequences of pollution events. However, common correlation measurements fail to capture the various properties of air pollution data, such as their non-normal distribution, heavy tails, and dynamic changes over time. Hence, they cannot generate highly accurate information. To overcome this issue, this study proposes a combination of the Generalized Autoregressive Conditional Heteroskedasticity model, Generalized Pareto distribution, and stochastic copulas as a tool to investigate the dependence structure between the PM<sub>10</sub> variable and other pollutant variables, including CO, NO<sub>2</sub>, O<sub>3</sub>, and SO<sub>2</sub>. Results indicate that the dynamic dependence structure between PM<sub>10</sub> and other pollutant variables can be described with a ranking of PM<sub>10</sub>–CO > PM<sub>10</sub>–SO<sub>2</sub> > PM<sub>10</sub>–NO<sub>2</sub> > PM<sub>10</sub>–O<sub>3</sub> for the overall time paths (<i>δ</i>) and the upper tail (<i>τ<sup>U</sup></i>) or lower tail (<i>τ<sup>L</sup></i>) dependency measures. This study reveals an evident correlation among pollutant variables that changes over time; such correlation reflects dynamic dependency.https://www.mdpi.com/2227-7390/8/11/1910copula modeldynamic dependencemultiple correlation measurementpollution risk assessment |
| spellingShingle | Nurulkamal Masseran Saiful Izzuan Hussain Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables Mathematics copula model dynamic dependence multiple correlation measurement pollution risk assessment |
| title | Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables |
| title_full | Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables |
| title_fullStr | Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables |
| title_full_unstemmed | Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables |
| title_short | Copula Modelling on the Dynamic Dependence Structure of Multiple Air Pollutant Variables |
| title_sort | copula modelling on the dynamic dependence structure of multiple air pollutant variables |
| topic | copula model dynamic dependence multiple correlation measurement pollution risk assessment |
| url | https://www.mdpi.com/2227-7390/8/11/1910 |
| work_keys_str_mv | AT nurulkamalmasseran copulamodellingonthedynamicdependencestructureofmultipleairpollutantvariables AT saifulizzuanhussain copulamodellingonthedynamicdependencestructureofmultipleairpollutantvariables |