Multivariate density forecast evaluation: A modified approach

We consider methods of evaluating multivariate density forecasts. Most previous studies use a stacked vector which is formed by the sequence of transformed marginal and conditional variables to evaluate density forecasts. However, these methods lack power when there is contemporaneous correlation among the variables. We propose a new method which is a location-adjusted version of that used by  Clements and Smith (2002) Some Monte Carlo simulations show that our test has a higher power than the previous methods in the literature. Two empirical applications also show the usefulness of our proposed test.