  Most common parametric families of copulas are totally ordered, and in many
cases they are also positively or negatively regression dependent and therefore
they lead to monotone regression functions, which makes them not suitable for
dependence relationships that imply or suggest a non-monotone regression
function. A gluing copula approach is proposed to decompose the underlying
copula into totally ordered copulas that combined may lead to a non-monotone
regression function.
