The Dynamic Conditional Correlation (DCC) model is one of the leading approaches in the literature for modeling time-varying correlation matrices. In the DCC framework the conditional correlation matrix is modeled as a function of the so called pseudo-correlation matrix, a symmetric positive-definite proxy of the conditional correlation matrix that, however, is not guaranteed to have a unit diagonal. Conditional correlations are then obtained by appropriately rescaling this matrix. In this work we propose a novel DCC specification based on an alternative normalization of the pseudo-correlation matrix called Projected DCC (Pro-DCC). Rather than rescaling, we propose projecting the pseudo-correlation matrix onto the set of correlation matrices in order to obtain the correlation matrix closest to that pseudo-correlation matrix. A simulation study shows that projecting performs better than rescaling when the dimensionality of the correlation matrix is large and the degree of dependence is high. An empirical application to the constituents of the S&P 100 shows that the proposed methodology performs favorably to the standard DCC in an out-of-sample asset allocation exercise.
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