Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices

This paper proposes a three-step estimation strategy for dynamic conditional correlation models. In the first step, conditional variances for individual and aggregate series are estimated by means of QML equation by equation. In the second step, conditional covariances are estimated by means of the polarization identity, and conditional correlations are estimated by their usual normalization. In the third step, the two-step conditional covariance and correlation matrices are regularized by means of a new non-linear shrinkage procedure and used as starting value for the maximization of the joint likelihood of the model. This yields the final, third step smoothed estimate of the conditional covariance and correlation matrices. Due to its scant computational burden, the proposed strategy allows to estimate high dimensional conditional covariance and correlation matrices. An application to global minimum variance portfolio is also provided, confirming that SP-DCC is a simple and viable alternative to existing DCC models.