Combining p-values for Multivariate Predictive Ability Testing

In this paper, we propose an intersection-union test for multivariate forecast accuracy based on the combination of a sequence of univariate tests. The testing framework evaluates a global null hypothesis of equal predictive ability using any number of univariate forecast accuracy tests under arbitrary dependence structures, without specifying the underlying multivariate distribution. An extensive Monte-Carlo simulation exercise shows that our proposed test has very good size and power properties under several relevant scenarios, and performs well in both low- and high dimensional settings. We illustrate the empirical validity of our testing procedure using a large dataset of 84 daily exchange rates running from 1 January 2011 to 1 April 2021. We show that our proposed test addresses inconclusive results that often arise in practice