A GARCH-Variance Dependent Approach to Modelize Dynamic Conditional Correlations

Modelling volatility in a multivariate framework has received many contributions in the recent literature, but problems in estimation are still frequently encountered when dealing with a large set of time series. The Dynamic Conditional Correlation (DCC) modelling is probably the most used approach; it has the advantage of separating the estimation of the variance of each time series (with great flexibility, using single univariate models) and the correlation part (with the strong constraint imposing the same dynamics to all the conditional correlations). We propose a modification to the DCC model, providing different dynamics for each conditional correlation, hypothesizing a dependence on the conditional variance of the time series. This new model implies adding only two parameters with respect to the DCC model, keeping the estimation simplicity and increasing the flexibility in applied cases. Its performance is evaluated on a real data set in terms of in-sample and out-of-sample forecasts with respect to other multivariate GARCH models. The results seem to favor the new model.