This paper develops bootstrap methods for testing whether, in a finite sample, competing out-of-sample forecasts from nested models are equally accurate. Most prior work on forecast tests for nested models has focused on a null hypothesis of equal accuracy in population — basically, whether...

We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class...

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 variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family proposed by...