Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations

We develop a methodology for testing the cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived, and approximate limit quantiles are tabulated. A sequential procedure to select the cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.