The impact of general non-parametric volatility functions in multivariate GARCH models

Recent studies have revealed that financial volatilities and correlations move together over time across assets and markets. The main effort has been on improving the flexibility of conditional correlation dynamics, while maintaining computational feasibility for large estimation problems. However, since in such models conditional covariances are the product of conditional correlations and individual volatilities, it is plausible that improving the estimation of individual volatilities will lead to better covariance forecasts, too. Functional gradient descent (FGD) has already been shown to improve substantially in-sample and out-of-sample covariance accuracy in the very simple constant conditional correlation (CCC) setting. Following this direction, the impact of FGD volatility estimates is tested in several multivariate GARCH settings, both at the multivariate and at the univariate portfolio levels. In particular, improving conditional correlations and improving individual volatilities are compared, to establish which effect produces the best fits and predictions for conditional covariances.