In this paper, we present a testing procedure for fractional orders of integration in the context of non-linear terms approximated by Fourier functions. The test statistic has an asymptotic standard normal distribution and several Monte Carlo experiments conducted in the paper show that it performs well in finite samples. Various applications using real life time series, such as US unemployment rates, US GNP and Purchasing Power Parity (PPP) of G7 countries are presented at the end of the paper.

中文翻译：

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使用傅立叶函数测试具有非线性平滑中断近似的分数单位根

在本文中，我们提出了在傅里叶函数近似的非线性项的上下文中积分分数阶的测试程序。检验统计量具有渐近标准正态分布，并且在论文中进行的几个蒙特卡罗实验表明它在有限样本中表现良好。文末介绍了使用现实生活时间序列的各种应用，例如美国失业率、美国 GNP 和 G7 国家的购买力平价 (PPP)。