Stationarity Testing Under Smooth Transition Trends : Asymptotics Results and Some Empirical Evidence

The effects on the standard LM stationarity test of an incorrect specification of an instantaneous break when the true data generating process displays a logistic trend are analysed via Monte Carlo simulations under three alternative models. A stationarity test is derived for the case of an exogeneously determined smooth transition trend obtaining its asymptotical distribution by the Fredholm approach. Our result permits any continuous and piecewise continuously differentiable sigmoid. An asymptotic power analysis for the proposed test (under logistic transition) is carried out, and results of a number of Monte Carlo simulations, designed with a view to analyse the behavior of the test in finite samples, are reported. The case when the nonlinear parameters are estimated is also considered, with a derivation of the test null asymptotic distribution and some simulations and sensibility analyses. The paper ends with an application to testing stationarity for the Nelson and Plosser (1982) series, and with the comparison of the conclusions for the stationarity of the series with results of previous works