This paper examines the finite-sample properties of the McAleer et al. (1988) tests of separate hypotheses within the context of the ARMA(p,q) family. Using two sets of Monte Carlo experiments, we find that (i) the orders of the identified process can substantially affect the empirical significance levels of both the separate model and separate prediction tests; and (ii) asymptotically most powerful separate tests can be dominated in finite samples by less powerful separate tests.