Unit root testing under a local break in trend
Unit root testing under a local break in trend
复制标题
局部趋势突破下的单位根检验
DOI：
10.1016/j.jeconom.2011.10.006
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发表时间：
2012
影响因子：
6.3
通讯作者：
Harvey D
中科院分区：
文献类型：
--
作者：
Harvey D
当不确定性存在于趋势中断的存在和时间上时，最近的检验单位根的方法采用中断检测方法，因此只有当某些辅助统计量检测到中断时才使用带中断的单位根检验。虽然这些方法在固定趋势中断和无趋势中断环境中都实现了接近渐近的效率，但在有限样本中，可以观察到测试的幂函数中明显的“谷”（当映射为中断幅度的函数时），对于非常小的中断，功率最初很高，然后随着中断幅度的增加而降低，然后再次增加。针对这一问题，我们提出了两种实用的解决方案，要么基于使用具有自适应临界值的带断单位根检验，要么基于带断和不带断单位根检验的拒绝联合原则。这些新程序被证明在有限的样本功率方面提供了更高的可靠性。对于现有的单位根统计量和新提出的单位根统计量，我们也发展了局部极限分布理论，将趋势断裂幅度视为局部到零。我们表明，该框架允许渐近分析接近有限样本幂谷现象，从而提供有用的分析见解。
Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in both fixed trend break and no trend break environments, in finite samples pronounced “valleys” in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem, we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without-break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights.