Johansen-type cointegration tests with a Fourier function

Abstract

This article extends the pioneering Johansen cointegration test to allow for structural breaks in a cointegration system. Instead of using usual dummy variables, we utilize a Fourier function to control for an unknown number of multiple breaks in the cointegration system. The underlying presumption of the procedure is that structural breaks often can be captured by using a small number of low-frequency components from a Fourier approximation. The number of parameters to estimate is reduced significantly, which can lead to a good performance of the tests. Monte Carlo simulations show that the new tests display good size and power properties, except for the cases of sharp breaks. Then, we consider a strategy using a union of rejections. The union test combines our suggested test with a test of the cointegration rank in VAR models in the presence of a possible break in trend at an unknown point. We further consider a procedure that selects a better model using a Schwarz-type criterion among Johansen, trend break-point, and Fourier models. The resulting test shows fairly correct sizes in all cases, including sharp breaks, smooth breaks, and no breaks. The power properties are also reasonable in almost all cases. © 2022 John Wiley & Sons Ltd.