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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.

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  • $\begingroup$ Just thinking out loud, x could be the return of stock X divided by recent (3 month?) volatility, or the residual in a GARCH model, etc. $\endgroup$ – Alex C Dec 6 '15 at 21:21
  • $\begingroup$ but when you fit a GARCH model $X_t = \sigma_tZ_t$ to some data X, then you need to specify the distribution of $Z_t$ when you are doing the fitting. Say you fit both X and Y to two GARCH models, how do you go about using copulas afterwards? $\endgroup$ – Erosennin Dec 6 '15 at 22:49
  • $\begingroup$ Have a look at Andrew's Pattons work on cupolas. He also provides a Matlab library to implement all his work. public.econ.duke.edu/~ap172/code.html $\endgroup$ – Tim Jan 31 '16 at 0:51

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