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英文文献：The Power of Unit Root Tests Against Nonlinear Local Alternatives-单位根检验对非线性局部替代的能力
英文文献作者：Matei Demetrescu,Robinson Kruse
英文文献摘要：
This article extends the analysis of local power of unit root tests in a nonlinear direction by considering local nonlinear alternatives and tests built specifically against stationary nonlinear models. In particular, we focus on the popular test proposed by Kapetanios et al. (2003, Journal of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason for such behavior is the interplay of nonstationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the "amount of nonlinearity"), rendering the linear test more powerful than the nonlinear one. Should however the error variance be small, the nonlinear test has better power against local alternatives. We illustrate this in an asymptotic framework of what we call persistent nonlinearity. The theoretical findings of this article explain previous results in the literature obtained by simulation. Furthermore, our own simulation results suggest that the user-specified adjustment scheme for deterministic components (e.g. OLS, GLS, or recursive adjustment) has a much higher impact on the power of unit root tests than accounting for nonlinearity, at least under local (linear or nonlinear) alternatives.
本文通过考虑局部非线性替代和针对平稳非线性模型建立的检验，将单位根检验的局部幂函数分析扩展到非线性方向。特别地，我们关注Kapetanios等人(2003年，《计量经济学杂志》112,359 -379)提出的流行检验，与线性Dickey-Fuller检验进行比较。为此，我们考虑确定性项的不同调整方案。我们提供渐近结果，表明误差方差对非线性情况下的测试行为有严重的影响;产生这种现象的原因是非平稳性和非线性的相互作用。特别地，我们表明，当误差方差中等或较大时(与“非线性量”相比)，数据生成过程的非线性可以渐近地忽略不计，从而使线性检验比非线性检验更有效。但在误差方差较小的情况下，非线性检验具有较好的抗局部替代能力。我们用渐近框架来说明这一点，我们称之为持续非线性。本文的理论结果解释了以往文献中通过模拟得到的结果。此外，我们自己的模拟结果表明，用户指定的确定性成分调整方案(如OLS、GLS或递归调整)对单位根检验的幂次的影响比考虑非线性要大得多，至少在局部(线性或非线性)替代方案下是这样的。
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