Multiplicative Conditional Correlation Models for Realized Covariance Matrices

Abstract

We introduce a class of multiplicative dynamic models for realized covariance matrices assumed to be conditionally Wishart distributed. The multiplicative structure enables consistent three-step estimation of the parameters, starting by covariance targeting of a scale matrix. The dynamics of conditional variances and correlations are inspired by specifications akin to the consistent dynamic conditional correlation model of the multivariate GARCH literature, and estimation is performed by quasi maximum likelihood. Simulations show that in finite samples the three-step estimator has smaller bias and root mean squared error than the full estimator when the cross-sectional dimension increases. An empirical application illustrates the flexibility of these models in a low-dimensional setting, and another one illustrates their effectiveness and practical usefulness in high dimensional portfolio allocation strategies.