Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We show how asymptotic results from the univariate case can be extended to multiple dimensions and how inference can be based on these results. Furthermore, we show that the novel instrumental variable procedure proposed by [20] (IVX) yields uniformly valid confidence regions for the entire autoregressive matrix. The results are applied to two specific examples for which we verify the theoretical findings and investigate finite sample properties in simulation experiments.

翻译：对于协整向量自回归过程，由于最小二乘估计量的渐近分布中存在某些不连续性，迄今为止难以实现均匀有效的推断。我们展示了如何将单变量情况下的渐近结果推广到多维情形，并说明了如何基于这些结果进行推断。此外，我们证明了[20]提出的新工具变量方法可针对整个自回归矩阵产生均匀有效的置信区域。我们将这些结果应用于两个具体示例，通过模拟实验验证了理论发现并研究了有限样本性质。