Multivariate forecast evaluation and rationality testing

"In this paper, we propose a new family of multivariate loss functions that can be used to test the rationality of vector forecasts without assuming independence across individual variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family recently proposed by Elliott, Komunjer, and Timmermann (2005). Following their methodology, we derive a GMM test for multivariate forecast rationality that allows the forecast errors to be dependent, and takes into account forecast estimation uncertainty. We use our test to study the rationality of macroeconomic vector forecasts in the growth rate in nominal output, the CPI inflation rate, and a short-term interest rate"--Federal Reserve Bank of St. Louis web site.