Copula-VAR and Copula-VAR-GARCH Modeling: Dangers for Value at Risk and Impulse Response Functions

Copulae have been recently proposed as a statistical tool to build flexible multivariate distributions, since they allow for a rich dependence structure and more flexible marginal distributions that better fit the features of empirical financial and economic data. Our extensive simulation studies investigate how misspecification in the marginals may affect the estimation of the dependence function represented by the copula and the effects of these biases for Value at Risk and Impulse Response Functions analysis. We show that the use of normal marginals when the true Data Generating Process is leptokurtic, produces biased estimates of the correlations. This may results in more aggressive Value at Risk estimates or in smaller confidence bands when computing Impulse Response Functions.