Robust out-of-sample inference

This paper presents analytical, empirical and simulation results concerning inference about the moments of nondifferentiable functions of out-of-sample forecasts and forecast errors. Special attention is given to the measurement of a modelʹs predictive ability using the test of equal mean absolute error. Tests for equal mean absolute error and mean square error are used to evaluate predictions of excess returns to the S & P 500 composite. Simulations indicate that appropriately constructed tests for equal mean absolute error can provide more accurately sized and more powerful tests than inappropriately constructed tests for equal mean absolute error and mean square error.