Approximate Conditional Unit Root Inference

Abstract

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.