Modeling Asymmetric Dependence Structure of Air Pollution Characteristics: A Vine Copula Approach

Abstract

Contaminated air is unhealthy for people to breathe and live in. To maintain the sustainability of clean air, air pollution must be analyzed and controlled, especially after unhealthy events. To do so, the characteristics of unhealthy events, namely intensity, duration, and severity are studied using multivariate modeling. In this study, the vine copula approach is selected to study the characteristics data. Vine copula is chosen here because it is more potent than the standard multivariate distributions, and multivariate copulas, especially in modeling the tails related to extreme events. Here, all nine different vine copulas are analyzed and compared based on model fitting and the comparison of models. In model fitting, the best model obtained is Rv123-Joint-MLE, a model with a root nodes sequence of 123, and optimized using the joint maximum likelihood. The components for the best model are the Tawn type 1 and Rotated Tawn type 1 180 degrees representing the pair copulas of (intensity, duration), and (intensity, severity), respectively, with the Survival Gumbel for the conditional pair copula of (duration, severity; intensity). Based on the best model, the tri-variate dependence structure of the intensity, duration, and severity relationship is positively correlated, skewed, and follows an asymmetric distribution. This indicates that the characteristic’s, including intensity, duration, and severity, tend to increase together. Using comparison tests, the best model is significantly different from others, whereas only two models are quite similar. This shows that the best model is well-fitted, compared to most models. Overall, this paper highlights the capability of vine copula in modeling the asymmetric dependence structure of air pollution characteristics, where the obtained model has a better potential to become a tool to assess the risks of extreme events in future work.

Keywords

• air pollution
• joint distribution
• multivariate modelling
• asymmetric copula
• vine copula