This paper examines the asymptotic and finite-sample properties of out-of-sample tests for equal accuracy and encompassing applied to nested models. These tests can be viewed as Granger causality tests. However, standard asymptotic critical values for many tests of equal accuracy and encompassing are invalid when models are nested rather than non-nested. Statistics such as those proposed by Diebold and Mariano (1995) and Harvey, et al. (1998) fail to converge to the standard normal distribution when the models are nested. Building on McCracken's (1999) results for equal accuracy tests, this paper derives the asymptotic distributions for a set of standard encompassing tests and one new encompassing test. Numerical simulations are used to generate the appropriate asymptotic critical values. Monte Carlo simulations are then used to evaluate the size and power of a battery of equal forecast accuracy and encompassing tests, as well as standard F-tests of causality. In these experiments, forecasts from an estimated VAR model are compared to those from a null estimated AR model. The simulation results indicate that McCracken's out-of-sample F-type test of equal accuracy and the encompassing test proposed in this paper can be more powerful than standard F-tests of causality. The Monte Carlo simulations also show that using invalid asymptotic critical values can produce misleading inferences. The paper also introduces a new encompassing test, the CM test, which scales the numerator of the HLN test by the variance of one of the forecast errors rather than an estimate of the variance of the covariance. The CM test is asymptotically normal under the null hypothesis. The paper also examines the ERIC test, which is based on a conditional efficiency regression and is asymptotically normal under the null hypothesis. The paper concludes that the CM and ERIC tests have the same limiting distribution under the null hypothesis. The paper also examines the Chong-Hendry (CH) test, which is based on an OLS regression and is asymptotically normal under the null hypothesis. The paper finds that the CM and ERIC tests have similar finite-sample properties to the HLN test. The paper also finds that the OOS F and CM tests perform well in finite samples, with only slight size distortions. The paper also finds that the asymptotically valid versions of the DM and ERIC tests and the CH test are modestly oversized in finite samples. The paper also finds that comparing the DM, HLN, and ERIC tests against invalid asymptotic critical values leads to too-infrequent rejections. The paper also finds that simple GC tests are sometimes slightly oversized when the number of observations is small, but about correctly sized otherwise. The paper concludes that the OOS F and CM tests are more powerful than standard F-tests of causality.This paper examines the asymptotic and finite-sample properties of out-of-sample tests for equal accuracy and encompassing applied to nested models. These tests can be viewed as Granger causality tests. However, standard asymptotic critical values for many tests of equal accuracy and encompassing are invalid when models are nested rather than non-nested. Statistics such as those proposed by Diebold and Mariano (1995) and Harvey, et al. (1998) fail to converge to the standard normal distribution when the models are nested. Building on McCracken's (1999) results for equal accuracy tests, this paper derives the asymptotic distributions for a set of standard encompassing tests and one new encompassing test. Numerical simulations are used to generate the appropriate asymptotic critical values. Monte Carlo simulations are then used to evaluate the size and power of a battery of equal forecast accuracy and encompassing tests, as well as standard F-tests of causality. In these experiments, forecasts from an estimated VAR model are compared to those from a null estimated AR model. The simulation results indicate that McCracken's out-of-sample F-type test of equal accuracy and the encompassing test proposed in this paper can be more powerful than standard F-tests of causality. The Monte Carlo simulations also show that using invalid asymptotic critical values can produce misleading inferences. The paper also introduces a new encompassing test, the CM test, which scales the numerator of the HLN test by the variance of one of the forecast errors rather than an estimate of the variance of the covariance. The CM test is asymptotically normal under the null hypothesis. The paper also examines the ERIC test, which is based on a conditional efficiency regression and is asymptotically normal under the null hypothesis. The paper concludes that the CM and ERIC tests have the same limiting distribution under the null hypothesis. The paper also examines the Chong-Hendry (CH) test, which is based on an OLS regression and is asymptotically normal under the null hypothesis. The paper finds that the CM and ERIC tests have similar finite-sample properties to the HLN test. The paper also finds that the OOS F and CM tests perform well in finite samples, with only slight size distortions. The paper also finds that the asymptotically valid versions of the DM and ERIC tests and the CH test are modestly oversized in finite samples. The paper also finds that comparing the DM, HLN, and ERIC tests against invalid asymptotic critical values leads to too-infrequent rejections. The paper also finds that simple GC tests are sometimes slightly oversized when the number of observations is small, but about correctly sized otherwise. The paper concludes that the OOS F and CM tests are more powerful than standard F-tests of causality.