Recent research has emphasised that permanent changes in the innovation variance (caused by structural shifts or an integrated volatility process) lead to size distortions in conventional unit root tests. Cavaliere and Taylor (2008) show how these size distortions may be resolved using the wild bootstrap. In this paper, we first derive the asymptotic power envelope for the unit root testing problem when the nonstationary volatility process is known. Next, we show that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that nonparametric estimation of the volatility process leads to the same asymptotic power envelope. Implementation of the resulting test involves cross-validation and the wild bootstrap. A Monte Carlo experiment shows that the asymptotic results are reflected in finite sample properties, and an empirical analysis of real exchange rates illustrates the applicability of the proposed procedures.

中文翻译：

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具有非平稳波动性的单位根的自适应野生引导测试

最近的研究强调，创新差异的永久性变化（由结构变化或综合的波动过程引起）会导致常规单位根检验中的尺寸失真。Cavaliere和Taylor（2008）展示了如何使用野生引导程序解决这些尺寸畸变。在本文中，当已知非平稳波动过程时，我们首先导出单位根检验问题的渐近功率包络。接下来，我们表明，在适当的条件下，就挥发性过程而言，从波动过程的非参数估计得出相同的渐近功率包络的意义上说，适应是可能的。生成的测试的实现涉及交叉验证和野引导。