In this paper, we use Monte Carlo (MC) testing techniques for testing lineariTY against smooth transition models. The MC approach allows us to introduce a new test that differs in two respects from the tests existing in the literature. First, the test is exact in the sense that the probabiliTY of rejecting the null when it is true is always less than or equal to the nominal size of the test. Secondly, the test is not based on an auxiliary regression obtained by replacing the model under the alternative by approximations based on a Taylor expansion. We also apply MC testing methods for size correcting the test proposed by Luukkonen, Saikkonen and Teräsvirta ("Biometrika", Vol. 75, 1988, p. 491). The results show that the power loss implied by the auxiliary regression-based test is non-existent compared with a supremum-based test but is more substantial when compared with the three other tests under consideration. Copyright 2006 Blackwell Publishing Ltd.
