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Super-exponential bubble model with stochastic mean-reverting critical times:Application in Chinese stock market

LIN Li,REN Ruo-en (School of Economics and Management,Beihang University,Beijing 100191,China)  
Bubbles are often defined as exponentially explosive prices within traditional financial bubble models.These models are bearing criticism to be not able to effectively detect the bubbles because the exponentially growing price regime observed,which is defined as bubble,could also be rationalized by some possible fundamental valuation models.However,super-exponential growth bubble models can provide a clear distinguishing signature between bubble and fundamental growth.In this kind of models,the essence of bubble reflects the faster-than-exponential characteristics,which implies a theoretical finite termination time.This paper attempted to introduce a new super-exponential growth bubble model,which is called Stochastic Mean-Reverting Critical Times model.According to this model,detection and diagnostic of bubble were translated into i) testing existence of a stationary mean-reverting critical times series embedded in nonlinear non-stationary stock price series,ii) estimation of exponent for positive feedback effects and the potential critical time.Employing this model,the empirical study for Chinese stock market indicates that the 2005-2007 Chinese bubble can be detected;the strength as well as stability of bubbles among 29 industrial sectors be also measured.Meanwhile,this model suggests the feasibility of advance bubble warning for Chinese stock market.At the last,this paper discusses the policy implication for bubble precaution.
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