Functional association measures among air quality index components

A widely used method for evaluating air quality is to represent the levels of pollutants using a singular metric defined as air quality index. Although widely used in the literature, a common criticism to air quality indexes is that they lack to account for variability among their components. This paper focuses on this aspect and emphasizes the importance of analyzing the association among pollutants by considering their variability over time. To this end, two original measures of association among pollutants are proposed using the functional data analysis approach. The suggested measures refer to two different aspects of association: the first refers to dispersion among pollutants and the second indicates closeness of pollutants to an alert threshold. The proposed association measures are evaluated through a simulation study and are applied to a real dataset of pollutant concentrations in the Tuscany region, in Central Italy.