Analytical Gradients of Dynamic Conditional Correlation Models

Abstract

We provide the analytical gradient of the full model likelihood for the Dynamic Conditional Correlation (DCC) specification by Engle (2002), the generalised version by Cappiello et al. (2006), and of the cDCC model by Aielli(2013). We discuss how the gradient might be further extended by introducing elements related to the conditional variance parameters, and discuss the issue arising from the estimation of constrained and/or reparametrised versions of the model. A computational simulation compares analytical versus numerical gradients, with a view to parameter estimation; we find that analytical differentiation yields more efficiency and improved accuracy.