Forecasting 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) modeling is probably the most used approach; it has the advantage of
separating the estimation of the volatility 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 correlations). We propose a modification to
the DCC model, providing different dynamics for each correlation, simply hypothesizing
a dependence on the volatility structure of each time series. This new model
implies adding only two parameters with respect to the original DCC model. Its performance
is evaluated in terms of out-of-sample forecasts with respect to the DCC
models and other multivariate GARCH models. The results on four data sets seem
to favor the new model.