Stationarity Testing Under Endogenous Smooth Deterministic Components: Some Asymptotic Results

Stationarity testing for time series which include a smooth trend with unknown parameters is considered in this paper. A pseudo-Lagrange Multiplier stationarity test is proposed and its asymptotic null distribution is obtained. The distribution depends on the unknown parameters of the model. Bootstrap techniques permit this problem to be circumvented, and the limiting percentiles of the statistic may be estimated consistently. The proposed procedure can be implemented without computer simulations. The theoretical proposal is complemented with a simulation study which allows us to check the performance of the test in finite samples. The paper ends with an empirical application.