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I don't know if this will help solve your convergence issue, but a standard way of incorporating conditional heteroskedasticity in copula models is to build a copula-GARCH model. Each time series is first modelled with GARCH, and then the standardized innovations from the GARCH models of all the series are jointly modelled with a copula.


If I remember e.g. McNeil et. al (2005: Proposition 5.29) correctly and if I understand you correctly, it should be possible to estimate the correlation parameter $\varrho$ of the Gaussian copula from two time series of the desired interest rates via calculating Kendall's $\tau$ or Spearman's rank correlation $\rho$ using the relationships: $\varrho = \sin(\...

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