Can anbody explain how Copulas are used to describe the dependency between, for example, the return on two different stocks?
I understand how Copulas are the "glue" that binds the two marginals together, from Sklar's theorem: $F(x,y) = C(G_{x}(x),G_{y}(y))$,
where X and Y are iid distributed. But in time series data X and Y are not iid. One has volatility change, dependence on yesterdays return etc.
How does one overcome this?
EDIT: I understand it has got something to do with modelling the residuals, correct? I'm looking for an idea, here.