Dynamic conditional angular correlation

Abstract

We introduce the concept of angular correlation for estimating the instantaneous correlation matrix with a single multivariate realization. The proposed estimator is generally a positive definite correlation matrix and robust in that for bivariate normal data, the sample angular correlation is equally likely to be above or below the population correlation coefficient. We then generalize the dynamic conditional correlation (DCC) model to the dynamic conditional angular correlation (DCAC) model. We demonstrate the efficacy and robustness of the proposed methods against leptokurticity, with some numerical experiments. In particular, a real application illustrates the better performance of the DCAC model than the DCC model in portfolio construction.