Asymmetric Unit Root Tests in the Presence of Innovation Variance Breaks: Threshold versus Consistent-Threshold Estimation

Kim et al. (2002) demonstrate that the Dickey-Fuller unit root test can experience severe size distortion when a large decrease in the innovation variance occurs early in the sample period, leading to spurious rejection of the null. We extend this analysis to the case of spurious identification of asymmetric stationarity by the MTAR test of Enders and Granger (1998) under similar circumstances. In terms of unit root testing, the properties of the MTAR test are inferior to those of the Dickey-Fuller test. However, the MTAR test with consistent-threshold estimation outperforms both the Dickey-Fuller and the original MTAR tests when considering the unit root hypothesis; size distortion being dramatically reduced. The consistent MTAR test is also to be preferred to the original MTAR test when testing the joint hypothesis of non-stationarity and symmetry since the original test can display considerable undersizing. However, the size of the consistent MTAR test is approximately nominal in all experiments except when extreme changes in innovation variance occur towards the beginning of the sample period.