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 extend asymptotic results from the univariate case to multiple dimensions and show how inference can be based on these results. Furthermore, we show that lag augmentation and a recent instrumental variable procedure can also yield uniformly valid tests and confidence regions. We verify the theoretical findings and investigate finite sample properties in simulation experiments for two specific examples.

翻译：协整向量自回归过程的统一有效推断因最小二乘估计量渐近分布中的某些不连续性而长期难以实现。我们将单变量情形下的渐近结果推广至多维情形，并阐明如何基于这些结果进行推断。此外，我们证明滞后增广方法与近期提出的工具变量程序同样能生成统一有效的检验与置信区域。通过两个具体实例的模拟实验，我们验证了理论发现并考察了有限样本性质。