英文文献：Bias-correction in vector autoregressive models: A simulation study-向量自回归模型中的偏置校正:一个仿真研究
英文文献作者：Tom Engsted,Thomas Q. Pedersen
英文文献摘要：
We analyze and compare the properties of various methods for bias-correcting parameter estimates in vector autoregressions. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that this simple and easy-to-use analytical bias formula compares very favorably to the more standard but also more computer intensive bootstrap bias-correction method, both in terms of bias and mean squared error. Both methods yield a notable improvement over both OLS and a recently proposed WLS estimator. We also investigate the properties of an iterative scheme when applying the analytical bias formula, and we ?find that this can imply slightly better fi?nite-sample properties for very small sample sizes while for larger sample sizes there is no gain by iterating. Finally, we also pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space during the process of correcting for bias.

分析比较了矢量自回归中各种校正偏置参数估计方法的性质。首先，我们证明现有文献中的两个解析偏差公式实际上是相同的。其次，通过详细的仿真研究，我们表明，这个简单易用的解析偏差公式，在偏差和均方误差方面，都优于更标准但更需要计算机密集的bootstrap偏差校正方法。这两种方法都比OLS和最近提出的WLS估计器有显著的改进。当应用解析偏差公式时，我们也研究了迭代方案的性质，我们发现这可以暗示更好的fi?对于非常小的样本容量，nite-sample属性，而对于较大的样本容量，迭代是没有增益的。最后，我们还特别关注了在偏差校正过程中，将原本平稳的模型推入参数空间非平稳区域的风险。