Approximate Conditional Unit Root Inference
基于Cox和Reid的调整方法，提出了高阶自回归模型中单位根似然比检验的修正，通过蒙特卡洛实验证明调整后的统计量能更快逼近渐近分位数。
Based on Cox and Reid (1987) adjustments of likelihood ratio (LR) tests for unit roots in higher‐order autoregressive models are proposed. While unit root inference does not fit directly into the framework of Cox and Reid, the ideas are applied in models with multi‐dimensional parameters of interest and only asymptotic orthogonality of parameters. The adjustments are very simple to apply in that they are of the degrees of freedom type. Detailed Monte Carlo experiments reveal that, for a wide range of admissible parameter values, adjusted LR statistics approximate the asymptotic percentiles of the unit root distributions at a much faster rate than unadjusted ones. In addition, the proposed adjustments are compared with simulated Bartlett type corrected LR tests. They behave equally well in a reasonable parameter region, while both fail on the boundary of the parameter region where an additional unit root is introduced.