Testing for Unit Roots in the Presence of a Possible Break in Trend and Non...

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英文文献：Testing for Unit Roots in the Presence of a Possible Break in Trend and Non-Stationary Volatility-在趋势和非平稳波动中存在可能的突破时对单位根的检验
英文文献作者：Giuseppe Cavaliere,David I. Harvey,Stephen J. Leybourne,A.M. Robert Taylor
英文文献摘要：
In this paper we analyse the impact of non-stationary volatility on the recently developed unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2008) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T??1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T1=2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, including, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this estimator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of various models of non-stationary volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models.

在这篇论文中，我们分析了非平稳波动对最近发展的单位根检验的影响，它允许在样本中一个未知点上发生趋势的可能突破，在Harris, Harvey, Leybourne和Taylor (2008) [HHLT]中考虑。HHLT的分析依赖于一种新的断裂分数估计器，当趋势发生断裂时，该估计器在率Op(T??1)下对真实断裂分数是一致的。然而，与其他可用估计器不同的是，当没有趋势断点时，HHLT估计器在速率Op(T1=2)下收敛于零。在他们的分析中，HHLT假设冲击遵循一个由IID创新驱动的线性过程。我们的第一个贡献是证明HHLT打破分数估计量保留相同的一致性属性的证明由HHLT IID情况很一般形式的创新显示不稳定的行为,包括,例如,一个在创新的波动可能会或可能不会发生的同时在趋势。然而，正如我们随后证明的，在非平稳波动存在的情况下，基于此估计量的单位根统计量的有限零分布并不是关键的。相关的蒙特卡罗证据被提出来量化非平稳波动的各种模型对这类测试的渐近和有限样本行为的影响。然后，通过考虑基于野bootstrap的HHLT测试实现，利用原始样本数据的趋势断点估计器，给出了一种对识别推理问题的解决方案。所提议的bootstrap方法不需要执行者为波动率指定一个参数模型，并且被证明在跨一系列模型的实践中表现得非常好。

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