Projected Dynamic Conditional Correlations

Abstract

We propose a novel specification of the Dynamic Conditional Correlation (DCC) model based on an alternative normalization of the pseudo-correlation matrix called Projected DCC (Pro-DCC). Our modification consists in projecting, rather than re-scaling, the pseudo-correlation matrix onto the set of correlation matrices in order to obtain a well defined conditional correlation matrix. A simulation study shows that projecting performs better than re-scaling when the dimensionality of the correlation matrix is large. 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.

Keywords: Multivariate Volatility, Dcc, Bregman Projection, Nearest-Correlation Matrix, Stein’s Loss

JEL Classification: C13, C32, C58, G11