  In this study, 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 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.
