On the asymptotic behavior of bubble date estimators
将Pang等人的三区制泡沫模型扩展为四区制，证明了两区制AR(1)模型中崩溃日期估计量的一致性，并发现恢复日期的极限行为取决于泡沫和恢复的程度。
In this study, we extend the three‐regime bubble model of Pang et al. (2021, Journal of Econometrics , 221(1):227–311) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date estimator in the two‐regime AR(1) model. The consistency allows us to split the sample before and after the date of collapse and to consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behavior of the recovery date varies depending on the extent of explosiveness and recovering.