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.

中文翻译：

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具有傅里叶函数的 Johansen 型协整检验

本文扩展了开创性的 Johansen 协整检验，以允许协整系统中的结构中断。我们不使用通常的虚拟变量，而是使用傅里叶函数来控制协整系统中未知数量的多重中断。该过程的基本假设是结构断裂通常可以通过使用来自傅里叶近似的少量低频分量来捕获。要估计的参数数量显着减少，这可以导致测试的良好性能。蒙特卡洛模拟表明，新测试显示出良好的尺寸和功率特性，但急剧断裂的情况除外。然后，我们考虑使用拒绝联合的策略。联合检验将我们建议的检验与 VAR 模型中的协整等级检验相结合，在未知点可能出现趋势突破的情况下。我们进一步考虑了一个程序，该程序使用约翰森、趋势断点和傅里叶模型中的施瓦茨类型标准选择更好的模型。结果测试在所有情况下都显示了相当正确的尺寸，包括急剧断裂、平滑断裂和无断裂。功率属性在几乎所有情况下也是合理的。