Financial bubble implosion and reverse regression - PHILLIPS, Peter C. B. (Institutional Knowledge at Singapore Management University, 2018)
Expansion and collapse are two key features of a financial asset bubble. Bubble expansionmay be modeled using a mildly explosive process. Bubble implosion may take several differentforms depending on the nature of the collapse and therefore requires some flexibility in modeling.This paper first strengthens the theoretical foundation of the real time bubble monitoringstrategy proposed in Phillips, Shi and Yu (2015a,b, PSY) by developing analytics and studyingthe performance characteristics of the testing algorithm under alternative forms of bubbleimplosion which capture various return paths to market normalcy. Second, we propose a newreverse sample use of the PSY procedure for detecting crises and estimating the date of marketrecovery. Consistency of the dating estimators is established and the limit theory addressesnew complications arising from the alternative forms of bubble implosion and the endogeneityeffects present in the reverse regression. A real-time version of the strategy is provided thatis suited for practical implementation. Simulations explore the finite sample performance ofthe strategy for dating market recovery. The use of the PSY strategy for bubble monitoringand the new procedure for crisis detection are illustrated with an application to the Nasdaqstock market.