Copulas to model non-monotonic dependency: an application on the relationship between temperature and mortality

The subject of this study is the use of copulas for modeling non-monotonic dependencies, to investigate the impact of temperatures on mortality. In particular, the paper employs a method for constructing copulas that can describe dependencies of arbitrary shape. The proposed methodology is based on the use of functions that preserve the uniform distribution. Compared to the existing literature, our methodology allows the construction of such functions in a parametric form, thus allowing for more flexible models that better adapt to describe the complexity of real phenomena. Considering that the relationship between mortality and temperature is not monotonic (low and high temperatures can both imply an increase in mortality rates) this proposal could be a proper alternative to model this demographic phenomenon.