On the Optimal Estimating Function Method for Conditional Correlation Models

We consider applying the optimal estimating function (OptEF) method to conditional correlation (CC) models for parameter estimation. This method is asymptotically more efficient than the Gaussian QML method under conditional nonnormality. This relative efficiency is obtained by exploiting the information of the multivariate conditional third and fourth moments, and is important because conditional nonnormality is a stylized fact of financial returns. We also demonstrate how to implement the OptEF method by updating the two-step variant of the Gaussian QML method under an independence assumption. This assumption requires that the true model be a constant CC model. Without this assumption, the updated statistic is still asymptotically valid, but can only be viewed as an approximation to the OptEF estimator. By focusing on the constant CC models with different dimensions, we also conduct a simulation study to confirm our theoretical results, and provide two empirical examples of dynamic spot-futures hedging and dynamic variance-minimum portfolios.