• Stationarity testing;
  • limiting distribution;
  • nonlinear time series;
  • nonlinear regression;
  • bootstrap;
  • Fredholm theory
  • C12;
  • C15;
  • C22

Stationarity testing for nonlinear time series models which include several smooth trend components with (possibly) unknown parameters is considered. A pseudo-Lagrange multiplier stationarity test is proposed and its asymptotic behaviour is derived. The limiting null distribution generally depends on the unknown parameters of the model. A bootstrap approach permits this problem to be circumvented and consistency of the bootstrapped test is obtained. The theoretical analysis is complemented with a simulation study which allows us to check the performance of the test in finite samples. The article ends with an empirical application.