The author proposes a class of exact tests of the null hypothesis of exchangeable forecast errors and, hence, of the hypothesis of no difference in the unconditional accuracy of two competing forecasts. The class includes analogues of the well-known Diebold and Mariano (1995) parametric and non-parametric test statistics. The forecast errors can be non-normal and contemporaneously correlated, and general forms of the loss function are admitted. The nonparametric distribution-free property of these new tests makes them robust to the presence of conditional heteroscedasticity, heavy tails, and outliers in the loss-differential series. These tests are used with a randomization or "Monte Carlo" resampling technique, which yields an exact and computationally inexpensive inference procedure. Simulations confirm the reliability of the new test procedure, and its power is found to be comparable with that of the size-corrected parametric Diebold-Mariano test. The test procedure is illustrated with an application to the term structure of interest rates. The application shows that exchangeable forecast errors can be found empirically even when comparing forecasts from estimated models.