Simulation-based finite-sample linearity test against smooth transition models

In this paper we use Monte Carlo testing techniques for testing linearity against the smooth transition models. The Monte Carlo approach allows us to introduce a new test that differs from the tests existing in the literature in two respects. First, the test is exact in the sense that the probability of rejecting the null when it is true is always less that or equal to the nominal size of the test. Second, 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 Monte Carlo testing methods for size-correcting the test proposed by Luukkonen Saikkonen and Teräsvirta (1988). Simulated annealing is used in computing values of the test statistics. The results show that the power loss implied by the auxiliary regression based test is nonexistent compared to a supremum-based test but is more substantial when compared to the other three tests under consideration.