A Copula-GARCH model

Abstract

In the present study we develop a new two-dimensional Copula-GARCH model. This type of twodimensional process is characterized by a dependency structure modeled using a copula function. For the marginal densities we employ a GARCH(1,1) model with innovations drawn from a t-Student distribution. The model can be easily extended by using more sophisticated processes for the marginal densities. The static specification of the model assumes that the dependency structure of the two data series does not vary in time implying that the parameters of the copula function are constant. On the other hand, the dynamic specification models explicitly the dynamics of these parameters. We econometrically estimate the parameters of the two specifications using various copula functions, focusing on the mixture between the Gumbel and Clayton copulas. We employ daily index returns from two emerging and two developed financial markets. The main finding is that including a varying dependency structure improves the goodness-of-fit of the Copula-GARCH model.