The Flexible Fourier Form and Local Generalised Least Squares De‐trended Unit Root Tests
将Elliott等人提出的局部GLS去趋势单位根检验推广到允许未知形式的确定性趋势函数中存在多种断点的情况，通过引入傅里叶近似提高了检验的稳健性，并证明了检验统计量具有良好的有限样本性质和稳定的非标准分布。
Abstract In two recent papers Enders and Lee (2009) and Becker, Enders and Lee (2006) provide Lagrange multiplier and ordinary least squares de‐trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this article, we generalize the unit root testing procedure based on local generalized least squares (GLS) de‐trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that the resulting unit root tests possess good finite sample size and power properties and the test statistics have stable non‐standard distributions, despite the curious result that their limiting null distributions exhibit asymptotic rank deficiency.