期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2009
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：A large number of parameterizations have been proposed to model conditional
variance dynamics in a multivariate framework. This paper examines the ranking
of multivariate volatility models in terms of their ability to forecast out-of-sample
conditional variance matrices. We investigate how sensitive the ranking is to
alternative statistical loss functions which evaluate the distance between the true
covariance matrix and its forecast. The evaluation of multivariate volatility models
requires the use of a proxy for the unobservable volatility matrix which may shift
the ranking of the models. Therefore, to preserve this ranking conditions with
respect to the choice of the loss function have to be discussed. To do this, we
extend the conditions defined in Hansen and Lunde (2006) to the multivariate
framework. By invoking norm equivalence we are able to extend the class of loss
functions that preserve the true ranking. In a simulation study, we sample data from
a continuous time multivariate diffusion process to illustrate the sensitivity of the
ranking to different choices of the loss functions and to the quality of the proxy. An
application to three foreign exchange rates, where we compare the forecasting
performance of 16 multivariate GARCH specifications, is provided.
关键词：volatility, multivariate GARCH, matrix norm and loss function, norm
equivalence.
