A Hierarchical Archimedean Copula (HAC) model for climatic variables: an application to Kenyan data - Otieno, Kevin; Chaba, Linda; Omondi, Evans; Odhiambo, Collins; Omolo, Bernard (Frontiers in Applied Mathematics and Statistics, 2025)
IntroductionAdvanced statistical modeling techniques, such as copula-based methods, have significantly improved the forecasting of weather variables by capturing dependencies between them. However, conventional copula approaches, such as the bivariate copula, often fail to capture complex interactions in high-dimensional climate data. This study aims to develop a multivariate joint distribution model for climatic variables using the Hierarchical Archimedean Copula (HAC) framework.MethodsParametric methods were used to fit marginal distributions to the six variables. The uniform variates were extracted using the inverse transformation technique. The structure and parameter estimation of HAC models were determined using the Recursive Maximum likelihood (RML) method. Model selection methods, Goodness of Fit (GOF) approaches, and graphical assessment were used to select the optimal HAC model.ResultsThe Weibull distribution was identified as the best fit for temperature, humidity, solar energy, and cloud cover, while the Gamma distribution was most suitable for wind, and the logistic distribution for sea-level pressure. For high-dimensional data, the HAC Frank copula demonstrated computational efficiency and effectively captured dependencies among variables.DiscussionThe HAC-Frank model offers a reliable and computationally efficient alternative for modeling high-dimensional climate dependencies, thereby providing a robust framework for climate forecasting, risk assessment, and environmental modeling.