## A comparison of the forecasting performances of multivariate volatility models

##### Abstract

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.