Comparison of the forecasting performances of multivariate volatility models

The consistent ranking of multivariate volatility models by means of statistical loss function is a challenging research field, because it concerns the quality of the proxy chosen to replace the unobserved volatility, the set of competing models to be ranked and the kind of loss function. The existent works only consider the ranking of multivariate GARCH (MGARCH) models, based on daily frequency of the returns. Less is known about the behaviour of the models that directly use the realized covariance (RCOV), the proxy that generally provides a consistent estimate of the unobserved volatility. The aim of this paper is to evaluate which model has the best forecast volatility accuracy, from a statistical and economic point of view. For the first point, we empirically rank a set of MGARCH and RCOV models by means of four consistent statistical loss functions. For the second point, we evaluate if these rankings are coherent with those resulting from the use of an economic loss function. The evaluation of the volatility models through the economic loss function is usually done by looking at the Value at Risk (VaR) measures and its violations. A violation occurs every time the portfolio losses exceed the VaR. To assess the performances of the volatility models from an economic point of view, different tests regarding the violations have been proposed. In this work, the unconditional and conditional tests are considered. The analysis is based on a Monte Carlo experiment that samples from a trivariate continuous-time stochastic process a vector of observation each five minutes per two years.