Efficient Factor GARCH Models and Factor-DCC Models

We reveal that in the estimation of univariate GARCH or multivariate generalized orthogonal GARCH (GO-GARCH) models, maximizing the likelihood is equivalent to making the standardized residuals as independent as possible. Based on that, we propose three factor GARCH models in the framework of GO-GARCH: independent-factor GARCH exploits factors that are statistically as independent as possible; factors in best-factor GARCH have the largest autocorrelation in their squared values such that their volatilities could be forecasted well by univariate GARCH; factors in conditionaldecorrelation GARCH are conditionally as uncorrelated as possible. A two-step method for estimating these models is introduced, and it gives easy and reliable estimation. Since the extracted factors may still have weak conditional correlations, we further propose factor-DCC models, as an extension to the above factor GARCH models with dynamic conditional correlation (DCC) modelling the remaining conditional correlations between factors. Experimental results on the Hong Kong stock market shows that conditional-decorrelation GARCH and independent-factor GARCH have better generalization performance than the original GO-GARCH, and that conditional-decorrelation GARCH (among factor GARCH models) and its extension with DCC embedded (among factor-DCC models) behave best.