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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). The authors 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.
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