Bootstrap Determination of the Co-Integration Rank in Vector Autoregressive Models
提出一种基于Bootstrap的似然比协整秩检验方法，通过受限参数估计生成满足原假设的样本，确保检验渐近正确且序贯选择秩小于真值的概率趋于零，蒙特卡洛模拟显示效果良好。
This paper discusses a consistent bootstrap implementation of the likelihood ratio \n(LR) co-integration rank test and associated sequential rank determination procedure \nof Johansen (1996). The bootstrap samples are constructed using the restricted parameter \nestimates of the underlying vector autoregressive (VAR) model that obtain under \nthe reduced rank null hypothesis. A full asymptotic theory is provided that shows that, \nunlike the bootstrap procedure in Swensen (2006) where a combination of unrestricted \nand restricted estimates from the VAR model is used, the resulting bootstrap data are \nI(1) and satisfy the null co-integration rank, regardless of the true rank. This ensures \nthat the bootstrap LR test is asymptotically correctly sized and that the probability that \nthe bootstrap sequential procedure selects a rank smaller than the true rank converges \nto zero. Monte Carlo evidence suggests that our bootstrap procedures work very well \nin practice.