A proposal of nonlinear cointegration test with the flexible Fourier approach

In this study, we propose a cointegration test in which structural changes are modeled gradually through the Fourier approach and the nonlinear structure is modeled with an exponential smooth transition autoregressive (ESTAR) model. In the traditional tests, structural changes are mostly modeled by dummy variables. However, the extended literature supposes that the flexible Fourier approach is an alternative approach to dummy variables since there is no need to know the form, date, and number of breaks with the Fourier approach. The lack of a cointegration test to combine the ESTAR model and Fourier approach in the literature constitutes the motivation of this study. Monte Carlo simulation results demonstrate that the size properties are close to the nominal size and the power of the test shows good performance even in the small sample simulation experiment. Results also indicate that the proposed test shows better power performance compared to the ESTAR cointegration test ignoring breaks.