This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy applied to direct, multi-step predictions from both non-nested and nested linear regression models. In contrast to earlier work -- including West (1996), Clark and McCracken (2001, 2005),and McCracken (2006) -- our asymptotics take account of the real-time, revised nature of the data. Monte Carlo simulations indicate that our asymptotic approximations yield reasonable size and power properties in most circumstances. The paper concludes with an examination of the real-time predictive content of various measures of economic activity for inflation.