On the asymptotic behavior of bubble date estimators

TL;DR

This paper extends a bubble model to include a fourth regime, providing asymptotic and finite sample justification for collapse date estimators, and analyzes the asymptotic behavior of recovery dates under different conditions.

Contribution

It introduces an extended bubble model with a new regime and establishes the consistency of collapse date estimators in a two-regime AR(1) framework.

Findings

Consistency of collapse date estimator proven

Asymptotic behavior of recovery date depends on explosiveness

Sample splitting enables separate estimation of exuberation and recovery dates

Abstract

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.