Fitting a Gaussian Copula with Student-t Marginal Returns

Summary

The document concerns modeling the log returns of two stocks with a Gaussian copula and Student-t marginal distributions. The author has already fit a Gaussian copula with normal margins and asks how to simulate data when the margins instead follow t distributions, including how to set their degrees of freedom while matching observed means and standard deviations.

One proposed approach is to generate multivariate normal pseudo-observations and transform them to t-distributed values, then estimate the degrees of freedom. The author is unsure whether this preserves the desired dependence and parameter fit. No answer, simulation results, or validation procedure is included, so the document identifies a modeling question rather than establishing a recommended implementation. It is useful as a prompt about separating dependence modeling from marginal distribution fitting, while leaving details such as parameterization and estimation unresolved.

Key ideas

• The model combines a Gaussian copula for dependence with Student-t distributions for individual return margins.
• The example concerns log returns for two stocks.
• The author asks how to fit t margins with chosen degrees of freedom and moments matching the data.
• Transforming multivariate normal pseudo-observations is proposed, but the document does not verify that approach.

Tags

# Gaussian Copula with t margins


# Gaussian Copula with t margins












I am trying to fit a Gaussian Copula with t margins to my data (log returns of two stocks). It has already worked for a Gaussian Copula with normal margins with:

normcopula_dist = mvdc(copula=normalCopula(normrho,dim=2), margins=c("norm","norm"), paramMargins=list(list(mean=db_mu, sd=db_sd), list(mean=cb_mu, sd=cb_sd)))

My question is, how can I simulate my data with t margins? Here I can only set a parameter for df, but I need a t distribution also with mean and standard deviation matching my copula. Any help here? My idea was to create multivariate normal pseudo observations and then to transform them into t distribution and use their df for the estimation, but I am not quite sure, if it worksfine.

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