Abstract

We extend the three-regime bubble model of Pang et al. (2021) 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 consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behaviour of the recovery date is different depending on the extent of the explosiveness and recovering.