Cointegration tests with gradual structural changes: A proposal of nonlinear cointegration test

The study aims to 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. It is seen that there is a great deficiency especially in cointegration tests with structural changes when we examine the literature on nonlinear time series models and cointegration tests developed based on these models. The lack of a cointegration test in the literature in which the breaks are modeled with the Fourier approach and the nonlinear structure is modeled with the ESTAR model constitutes the motivation of this study. In order to create a substructure for the test proposed in the study, first of all, nonlinear models in mean are explained and theoretical literature evaluation is made on unit root and cointegration tests. We examine the size and power properties with Monte Carlo simulations subsequent to evaluation of the theoretical literature. The results show that the size does not depend on the degree of the variance and the serial correlation of the error term. The size of the test is close to the nominal level at different observation and Fourier frequencies. We observe that the proposed test shows good power properties, especially at low level Fourier frequencies. The power of the test increases depending on the increase in the observation values. The size and power properties of the test give good results in a small sample compared to other tests suggested in the literature. We use grid search instead of Taylor expansion to overcome the identification problem of the nuisance parameter. In addition to the simulation results, we give an empirical example to show the steps of the proposed test. In the empirical example where we seek an answer to the question "Is there a cointegration relationship between globalization and air transport in Turkey?", the null hypothesis which refers to no cointegration relation is not rejected when structural changes are not taken into account but, however, we reject the null hypothesis with the proposed test which models the changes with Fourier approach. The empirical example results prove that results tend to be biased when we do not consider the structural changes.