Multivariate Forecast Evaluation and Rationality Testing

In this paper, we propose a new family of multivariate loss functions to test the rationality of vector forecasts without assuming independence across variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family proposed by Elliott, Komunjer, and Timmerman (2008). Following their methodology, we derive~a GMM test for multivariate forecast rationality that allows the forecaster's loss to be nonseparable across variables and takes into account forecast estimation uncertainty. We use our test to study the joint rationality of macroeconomic forecasts in the growth rate of nominal output, CPI inflation rate, and short-term interest rate.