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What is Learnable in Valiant's Theory of the Learnable? 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On the asymptotic behavior of bubble date estimators
Eiji Kurozumi, Anton Skrobotov · 2021-10-09 · via math.ST updates on arXiv.org

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.

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