This paper examines the asymptotic and finite-sample properties of out-of-sample tests for equal forecast accuracy and encompassing when applied to nested models. Standard asymptotic critical values for many tests, such as those proposed by Diebold and Mariano (1995) and Harvey et al. (1998), are invalid when models are nested. The paper derives the asymptotic distributions for a set of standard encompassing tests and introduces a new encompassing test. Numerical simulations generate appropriate asymptotic critical values, and Monte Carlo simulations evaluate the size and power of these tests compared to standard F-tests of causality. The results indicate that the out-of-sample F-type test of equal accuracy and the new encompassing test can be more powerful than standard F-tests of causality. Using invalid asymptotic critical values can lead to misleading inferences. The paper also applies these tests to determine whether unemployment rate has predictive power for inflation in quarterly U.S. data.This paper examines the asymptotic and finite-sample properties of out-of-sample tests for equal forecast accuracy and encompassing when applied to nested models. Standard asymptotic critical values for many tests, such as those proposed by Diebold and Mariano (1995) and Harvey et al. (1998), are invalid when models are nested. The paper derives the asymptotic distributions for a set of standard encompassing tests and introduces a new encompassing test. Numerical simulations generate appropriate asymptotic critical values, and Monte Carlo simulations evaluate the size and power of these tests compared to standard F-tests of causality. The results indicate that the out-of-sample F-type test of equal accuracy and the new encompassing test can be more powerful than standard F-tests of causality. Using invalid asymptotic critical values can lead to misleading inferences. The paper also applies these tests to determine whether unemployment rate has predictive power for inflation in quarterly U.S. data.