In this paper, we introduce the notion of dynamic copulas to model serial dependence as well as interdependence between several time series. The proposed methodology is totally different from the usual time-varying copula modeling of time series in which only the dependence between the serially independent innovations is taken into account and time series must be modeled individually. Here no modeling of univariate time series in necessary and we tackle at the same time serial dependence and interdependence. We discuss issues related to parameter estimation as well as tests of goodness-of-fit. We treat in greater detail two families, specifically the meta-elliptic copulas and Archimedean copulas. The methodology is then applied to model the dynamic dependence between the Canadian/US exchange rate and value of oil futures during the last ten years.
Published March 2010 , 26 pages