We examine a class of popular structural models of exchange rate determination and compare them to a random walk with and without drift. Given almost any set of conditioning variables, we find parametric specifications fail. Our findings are based on a broad entropy function of the whole distribution of variables and forecasts. We also find significant evidence of nonlinearity and/or “higher moment” influences which seriously questions the habit of forecast and model evaluation based on mean-variance criteria. Taylor rule factors may improve out of sample “forecasts” for some models and exchanges, but do not offer similar improvement for in-sample (historical) fit. We estimate models of exchange rate determination nonparametrically so as to avoid functional form issues. Taylor rule and some other variables are smoothed out, being statistically irrelevant in sample. The metric entropy tests suggest significant differences between the observed densities and their in- and out- of sample forecasts and fitted values. Much like the Diebold-Mariano approach, we are able to report statistical significance of the differences with our more general measures of forecast performance.