英文文献：Co-integration Rank Testing under Conditional Heteroskedasticity-条件异方差下的协整秩检验
英文文献作者：Giuseppe Cavaliere,Anders Rahbek,A.M.Robert Taylor
英文文献摘要：
We analyse the properties of the conventional Gaussian-based co-integrating rank tests of Johansen (1996) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either i.i.d. or (strict and covariance) stationary martingale difference innovations. We then propose wild bootstrap implementations of the co-integrating rank tests and demonstrate that the associated bootstrap rank statistics replicate the first-order asymptotic null distributions of the rank statistics. We show the same is also true of the corresponding rank tests based on the i.i.d. bootstrap of Swensen (2006). The wild bootstrap, however, has the important property that, unlike the i.i.d. bootstrap, it preserves in the re-sampled data the pattern of heteroskedasticity present in the original shocks. Consistent with this, numerical evidence suggests that, relative to tests based on the asymptotic critical values or the i.i.d. bootstrap, the wild bootstrap rank tests perform very well in small samples under a variety of conditionally heteroskedastic innovation processes. An empirical application to the term structure of interest rates is given.

摘要分析了Johansen(1996)的基于高斯的协整秩检验的性质，证明了被检验序列的向量是由全局平稳的条件异方差(鞅差)创新驱动的。我们首先证明秩统计量的极限零分布与先前作者假设i.i.d.或(严格和协方差)平稳鞅差分创新的结果一致。然后，我们提出了协整秩检验的野自举实现，并证明了相关的自举秩统计量复制秩统计量的一阶渐近零分布。我们表明，基于Swensen(2006)的i.i.d. bootstrap的相应等级检验也是如此。然而，野自举法有一个重要的性质，与i.i.d.自举法不同，它在再采样数据中保留了原始冲击中存在的异方差模式。与此相一致的是，数值证据表明，相对于基于渐近临界值或i.i.d. bootstrap的检验，在各种条件异方差创新过程下，野bootstrap秩检验在小样本中表现得很好。给出了利率期限结构的一个实证应用。