Determining the optimal dimensionality of multivariate volatility models with tools from random matrix theory

We present a brief review of methods from random matrix theory (RMT), which allow to gain insight into the problem of estimating cross-correlation matrices of a large number of financial assets. These methods allow to determine the optimal number of principal components or factors for the description of correlations in such a way that only statistically relevant information is used. As an application of this method, we suggest two classes of multivariate GARCH-models which are both easy to estimate and perform well in forecasting the multivariate volatility process for more than 100 stocks.